Question

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

g(x) = a(x² + 1) – x(a² + 1)

Answer 1

`g(x)=a[(x^2+1)-x(a^2+1)]^2=ax^2+a-a^2x-x`

`=ax^2-[(a^2+1)-x]+0=ax^2-a^2x-x+a`

`=ax(x-a)-1(x-a)=(x-a)(ax-1)`

Zeros of the polynomials `=1/a` and a

Sum of zeros `=(-(a^2-1))/a`

`rArr1/a+a=(a^2+1)/a`

`rArr(a^2+1)/a=(a^2+1)/a`

Product of zeros `=a/a`

`rArr1/axxa=a/a`

`rArr1=1`

Hence relationship verified.