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Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

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Given : Sum of zeroes = (∝ + β) = 8

Product of the zeroes = = 12

Required quadratic polynomial is

x2 – (∝+β)x + ∝β 

= x2 – (8)x + 12

Now, find the zeroes of the above polynomial.

Let f(x) = x2 – (8)x + 12

= x2 – 6x – 2x + 12

= (x -6)(x – 2)

Substitute f(x) = 0.

either (x -6) = 0 or (x – 2) = 0

 x = 6 or x = 2

2 and 6 are the zeroes of the polynomial.

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