If the zeros of the polynomial f(x)=k2x2−17x+k+2,(k>0) are reciprocal of each other, then the value of k is
A
2
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B
−1
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C
−2
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D
1
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Solution
The correct option is A2 Let α and 1α be the roots of k2x2−17x+(k+2) So, product of roots =α×1α ⇒α×1α=k+2k2 ⇒k2=k+2 ⇒k2−k−2=0 ⇒k=2 and k=−1 But k>0,∴k=2 Hence, option A is the correct answer.