Q14 of 25 Page 2

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:


For a quadratic polynomial,


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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