Q. 2 E3.7( 3 Votes )

# Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:

x^{2} – (2a + b)x + 2ab

Answer :

Let f(x) = x^{2} – (2a + b)x + 2ab

f(x) = x^{2} – 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 x^{2} – (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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