Question

find zero of polynomial and verify the relationship between the zero and their coefficient
g (x) = a (x² + 1) - x (a² + 1)​

Answer 1

Answer:

Given,

g(x) = a(x2+1) – x(a2+1)

We put g(x) = 0

⇒ a(x2+1)–x(a2+1) = 0

⇒ ax2 + a − a2x – x = 0

⇒ ax2 − a2x – x + a = 0

⇒ ax(x − a) − 1(x – a) = 0

⇒ (x – a)(ax – 1) = 0

This gives us 2 zeros, for

x = a and x = 1/a

Hence, the zeros of the quadratic equation are a and 1/a.

Now, for verification

Sum of zeros = – coefficient of x / coefficient of x2

a + 1/a = – (-(a2 + 1)) / a

(a2 + 1)/a = (a2 + 1)/a

Product of roots = constant / coefficient of x2

a x 1/a = a / a

1 = 1

Therefore, the relationship between zeros and their coefficients is verified.Read more on Sarthaks.com - https://www.sarthaks.com/623563/g-x-a-x-2-1-x-a-2-1