Question

Find the zeroes of the quadratic polynomials x² – (2a + b)x + 2ab and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = x² – (2a + b)x + 2ab

f(x) = x² – 2ax – bx + 2ab

= x(x – 2a) – b(x – 2a)

= (x – 2a) (x – b)

On putting f(x) = 0 , we get

(x – 2a) (x – b) = 0

⇒ x – 2a = 0 or x – b = 0

⇒x = 2a or x = b

Thus, the zeroes of the given polynomial x² – (2a + b)x + 2ab are 2a and b

Verification

Sum of zeroes = α + β = 2a + b or

So, the relationship between the zeroes and the coefficients is verified.