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.

Obtain the zeroes of the polynomial 7 x2 + 18 x – 9 Hence, write a polynomial each of whose zeroes is twice

The sum of the squares of two consecutive natural numbers is 365. Find the numbers.

Find the value of c for which the quadratic equation (c + 1) y2 – 6(c+1) y + 3(c+9)= 0

The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took

If a, b are the zeroes of polynomial f(x)=x² – p (x+1) – c then show that (a+1) (b+1)= 1 – c

Find x in terms of a b, and c: a/(x – a) + b/(x – b) = 2 c/(x – c), x ≠ a, b, c

Find the value of k for which the quadratic equation (k + 1) y2 – 6(k +1) y + 3(k +9)= 0

Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2

Solve the quadratic equation: 2x^2 – 7x + 3 = 0

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.

Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial.

If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of 𝛼/𝛽 + 𝛽 /𝛼.

Find the value of c for which the quadratic equation (c + 1) y2 – 6(c+1) y + 3(c+9)= 0

If 𝛼 and 𝛽 are zeroes of a polynomial 6 𝑥2 – 5x + 1 then form a quadratic polynomial whose zeroes are 𝛼2 and 𝛽2.

Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship

In a flight of 2800 km, an aircraft was slowed down due to bad weather.

A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article.

Two water taps together can fill a tank in 3 1/3 hours.

Find the zeroes of the polynomial f(t) = t2 + 4 √3 t – 15 and verify the relationship

If 𝛼, β are zeroes of quadratic polynomial f(x) = 6x 2 + 11x – 10, find the value of 𝛼/𝛽 + 𝛽 /𝛼.

Solve for x : 4/x – 5 / (2x + 3) = 3

The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers.

The graph of the polynomial = ax2+bx+c is shown below. Write the signs of ‘a’ and ‘b2-4ac’

Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9)= 0

If 𝛼, β are zeroes of quadratic polynomial x 2 – 2x + 3, find the polynomial whose roots are

Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than

If 𝛼, β are zeroes of quadratic polynomial 5x 2 + 5x + 1, find the value of 1. 𝛼2 + 𝛽2 2. 𝛼-1 + 𝛽-1

Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.

Find the discriminant of the quadratic equation 4x^2 – 5 = 0 and hence comment on the nature of the equation.

Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots.

Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0.

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.