PolynomialsImportant Questions 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 »
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 »
