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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)

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#### APPEARS IN

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