Q. 2 E3.7( 3 Votes )

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

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

Product of zeroes = αβ = 2a × b = 2ab or

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

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