Question

if one zero of p(x)=(a^2+4)x^2+13x+4a is reciprocal of others,find the value of a

Answer 1

I hope it will help you

Answer 2

Hey.

Here is the answer.

Let one zero be z

then other zero will be 1/z

as sum of zeros = -(coefficient of x/coefficient of x^2)

Also , product of zeros = constant / coefficient of x^2

so, 1/z × z = 4a/(a^2+4)

or, 1 = 4a/(a^2 + 4)

or, a^2+4 = 4a

or, a^2 + 4 -4a = 0

or, a^2 -2a -2a + 4 = 0

or, a(a-2) -2(a-2) = 0

or, (a-2)(a-2) = 0

so, a = 2.

Thanks.