Question

if one of the zeros of (a^4+4)x²+13x+4a find a​

Answer 1

Now let one of the roots be A. Then according to question the other root must be 1/A.

Now we know that

Product of roots = constant term of quadratic equation/(coefficient of x²)

Putting values we get

A x 1/A = 4a/(a² + 4) = 1 = 4a/(a² + 4)

= a² + 4 = 4a = a² - 4a + 4 = 0 ( rearranging above equation)

= a² - 2a - 2a + 4 = 0 = a(a - 2) - 2(a - 2) = 0

= (a - 2)(a - 2) = 0 = (a - 2)² =0

= a - 2 = 0 = a = 2