PolynomialsImportant Questions 37. An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial p(x)= – 0.0025 x ^ 2 – 0.025 x + 136 Read More » 23. Verify that roots of the quadratic equation (p − q) x2 + (q − r) x + (r − p) = 0 are equal when q + r = 2p. Read More » 24. α, β are zeroes of the polynomial p(x) = 3×2 − 6x − 5. Find the value of 1/α2 + 1/β2. Read More » 37. During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial p(x) = – x2 + 2x + 8, where x is the length (in feet) on stage level. Read More » 21. If α, β are the zeroes of the polynomial p(x) = x^2 − 3x − 1, then find the value of 1/α +1/β. Read More » 24. Find a quadratic polynomial whose zeroes are (5-2√3) and (5+2√3). Read More » 35 b. The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle. Read More » 35 a. In a class test, the sum of Anamika’s marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects. Read More » 33 b. The area of a right-angled triangle is 600 cm². If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle. Read More » 21. If α, ẞ are the zeroes of the quadratic polynomial p x ^ 2 + qx + r then find the value of α³ β + β³α. Read More » 24. Find the value of p, for which one zero of the quadratic polynomial p x ^ 2 – 14 x + 8 is 6 times the other. Read More » 34 a. In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight. Read More » 34 b. Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool. Read More » While factorizing a given polynomial, using remainder & factor theorem, a student finds Read More » Find the zeroes of the quadratic polynomial 2 x^2 – (1 + 2√2) x + √2 and verify the relationship between zeroes and coefficients of the polynomial. Read More » Obtain the zeroes of the polynomial 7 x2 + 18 x – 9 Hence, write a polynomial each of whose zeroes is twice Read More » The sum of the squares of two consecutive natural numbers is 365. Find the numbers. Read More » Find the value of c for which the quadratic equation (c + 1) y2 – 6(c+1) y + 3(c+9)= 0 Read More » While factorizing a given polynomial, a student finds that (2x + 1) is a factor of Read More » A brooch is a small piece of jewellery which has a pin at the back so it can be Read More » The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took Read More » If a, b are the zeroes of polynomial f(x)=x² – p (x+1) – c then show that (a+1) (b+1)= 1 – c Read More » Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball Read More » Find x in terms of a b, and c: a/(x – a) + b/(x – b) = 2 c/(x – c), x ≠ a, b, c Read More » The volume of water in a rectangular, in-ground, swimming pool is given by V (x)= Read More » Find the value of k for which the quadratic equation (k + 1) y2 – 6(k +1) y + 3(k +9)= 0 Read More » An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended Read More » The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial Read More » Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2 Read More » Solve the quadratic equation: 2x^2 – 7x + 3 = 0 Read More » Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k + 1) x + (8 k + 1) = 0 has real and equal roots. Read More » Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Read More » If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of 𝛼/𝛽 + 𝛽 /𝛼. Read More » Find the value of c for which the quadratic equation (c + 1) y2 – 6(c+1) y + 3(c+9)= 0 Read More » A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, Read More » If 𝛼 and 𝛽 are zeroes of a polynomial 6 𝑥2 – 5x + 1 then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2. Read More » Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship Read More » In a flight of 2800 km, an aircraft was slowed down due to bad weather. Read More » A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. Read More » Two water taps together can fill a tank in 3 1/3 hours. Read More » While playing in a garden, Samaira saw a honeycomb and asked her mother what is that. Read More » A ball is thrown in the air so that t seconds after it is thrown, its height h metre above Read More » Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship Read More » If 𝛼, β are zeroes of quadratic polynomial f(x) = 6x 2 + 11x – 10, find the value of 𝛼/𝛽 + 𝛽 /𝛼. Read More » Solve for x : 4/x – 5 / (2x + 3) = 3 Read More » The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers. Read More » The graph of the polynomial = ax2+bx+c is shown below. Write the signs of ‘a’ and ‘b2-4ac’ Read More » Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9)= 0 Read More » If 𝛼, β are zeroes of quadratic polynomial x 2 – 2x + 3, find the polynomial whose roots are Read More » Raj and Ajay are very close friends. Both the families decide to go to Read More » Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less Read More » A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than Read More » If 𝛼, β are zeroes of quadratic polynomial 5x 2 + 5x + 1, find the value of 1. 𝛼2 + 𝛽2 2. 𝛼-1 + 𝛽-1 Read More » In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water Read More » Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. Read More » Find the discriminant of the quadratic equation 4x^2 – 5 = 0 and hence comment on the nature of the equation. Read More » Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Read More » Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0. Read More » If one zero of the polynomial p(x) = 6x^2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Read More »
37. An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial p(x)= – 0.0025 x ^ 2 – 0.025 x + 136 Read More »
23. Verify that roots of the quadratic equation (p − q) x2 + (q − r) x + (r − p) = 0 are equal when q + r = 2p. Read More »
24. α, β are zeroes of the polynomial p(x) = 3×2 − 6x − 5. Find the value of 1/α2 + 1/β2. Read More »
37. During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the polynomial p(x) = – x2 + 2x + 8, where x is the length (in feet) on stage level. Read More »
21. If α, β are the zeroes of the polynomial p(x) = x^2 − 3x − 1, then find the value of 1/α +1/β. Read More »
35 b. The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle. Read More »
35 a. In a class test, the sum of Anamika’s marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects. Read More »
33 b. The area of a right-angled triangle is 600 cm². If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle. Read More »
21. If α, ẞ are the zeroes of the quadratic polynomial p x ^ 2 + qx + r then find the value of α³ β + β³α. Read More »
24. Find the value of p, for which one zero of the quadratic polynomial p x ^ 2 – 14 x + 8 is 6 times the other. Read More »
34 a. In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight. Read More »
34 b. Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool. Read More »
Find the zeroes of the quadratic polynomial 2 x^2 – (1 + 2√2) x + √2 and verify the relationship between zeroes and coefficients of the polynomial. Read More »
Obtain the zeroes of the polynomial 7 x2 + 18 x – 9 Hence, write a polynomial each of whose zeroes is twice Read More »
If a, b are the zeroes of polynomial f(x)=x² – p (x+1) – c then show that (a+1) (b+1)= 1 – c Read More »
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball Read More »
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended Read More »
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial Read More »
Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k + 1) x + (8 k + 1) = 0 has real and equal roots. Read More »
Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Read More »
A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, Read More »
If 𝛼 and 𝛽 are zeroes of a polynomial 6 𝑥2 – 5x + 1 then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2. Read More »
A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. Read More »
A ball is thrown in the air so that t seconds after it is thrown, its height h metre above Read More »
If 𝛼, β are zeroes of quadratic polynomial f(x) = 6x 2 + 11x – 10, find the value of 𝛼/𝛽 + 𝛽 /𝛼. Read More »
The graph of the polynomial = ax2+bx+c is shown below. Write the signs of ‘a’ and ‘b2-4ac’ Read More »
If 𝛼, β are zeroes of quadratic polynomial x 2 – 2x + 3, find the polynomial whose roots are Read More »
Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less Read More »
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than Read More »
If 𝛼, β are zeroes of quadratic polynomial 5x 2 + 5x + 1, find the value of 1. 𝛼2 + 𝛽2 2. 𝛼-1 + 𝛽-1 Read More »
In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water Read More »
Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. Read More »
Find the discriminant of the quadratic equation 4x^2 – 5 = 0 and hence comment on the nature of the equation. Read More »
Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Read More »
If one zero of the polynomial p(x) = 6x^2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Read More »
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