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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
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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