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Question

If k is ratio of zeroes of the polynomial 4x25x3, then the value of (k+1k)2 is

A
4912
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B
1249
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C
1442401
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D
2401144
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Solution

The correct option is C 1442401
Given polynomial is 4x25x3, and k is the ratio of its zeroes.

Let α and β be the zeroes of the polynomial, then k=αβ.

Also, α+β=(5)4=54

and, αβ=34

Now, k+1k=αβ+βα (k=αβ)

=α2+β2αβ

=(α+β)22αβαβ

=(54)22×(34)(34) (α+β=54; αβ=34)

=2516+32(34)

=4912

(k+1k)2=(4912)2

=(1249)2

=1442401

Thus, the value of (k+1k)2 is 1442401.

Hence, the correct answer is option (c).

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