MCQ

If one zero of the polynomial *f*(*x*) = (*k*^{2} + 4)*x*^{2} + 13*x* + 4*k* is reciprocal of the other, then *k*=

#### Options

2

-2

1

-1

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#### Solution

We are given *f*(*x*) = (*k*^{2} + 4)*x*^{2} + 13*x* + 4*k* 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)

Concept: Concept of Polynomials

Is there an error in this question or solution?

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