# Find the zeroes of g(x) = a(x2 + 1) – x(a2 + 1) and verify the relationship between zeroes of polynomial and its coefficient.

Concept Used:

P(x) = ax2 + bx + c

Sum of the roots

The product of roots

Given: g(x) = a(x2 + 1) – x(a2 + 1)

Explanation:

g(x) = ax2 – a2x – x + a

g(x) = ax2 – (a2 + 1)x + a

g(x) = ax(x – a) –1(x – a)

g(x) = (ax – 1) (x – a)

For zeros of g(x), g(x) = 0

(ax – 1) (x – a) = 0

Therefore,

Sum of the zeroes

The product of the zeroes

Hence, Verified.

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