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If One Zero of the Polynomial F(X) = (K2 + 4)X2 + 13x + 4k is Reciprocal of the Other, Then K = - Mathematics

MCQ

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

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Solution

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)

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Q 3 | Page 61
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