Question

If one zero of the polynomial f(x) = (k² + 4)x² + 13x + 4k is reciprocal of the other, then k=

Options

• 2

• -2

• 1

• -1

Answer 1

We are given  f(x) = (k² + 4)x² + 13x + 4k then

`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`

`= (-13)/(k^2+4)`

`alpha xxbeta = (\text{constat term})/(text{coefficient of} x^2)`

`= (4k)/(k^2+4)`

One root of the polynomial is reciprocal of the other. Then, we have

`alpha xxbeta`

`⇒ (4k)/(k^2+4)=1`

`⇒  k^2 - 4k +4 =0`

`⇒ (k -2)^2 =0`

`⇒ k =2`

Hence the correct choice is (a)