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If the zeroes of the polynomial $f (x) = k^{2} x^{2} - 17 x + k + 2, k > 0$ are reciprocal of each other, then the value of k is

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-1

-2

answer is A.

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Detailed Solution

Given, the zeroes of the polynomial

f (x) = k^{2} x^{2} - 17 x + k + 2, k > 0

are reciprocal of each other.
We need to find the value of k.
Using the formula,
Product of roots of equation

a x^{2} + bx + c

is equal to

\frac{c}{a} .

Assume (

α, \frac{1}{α}

) be the roots of

k^{2} x^{2} - 17 x + k + 2

.
Then, solving the equation,

α \times \frac{1}{α} = \frac{k + 2}{k^{2}}

\Rightarrow k^{2} = k + 2

\Rightarrow k^{2} - k - 2 = 0

\Rightarrow (k - 2) (k + 1) = 0

\Rightarrow k = 2

and

k = - 1

From the given data,

k > 0 .

∴ k = 2

.
Hence, the correct option is 1.

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