Q2 of 90 Page 2

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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