For a given value of $k$ the product of the roots of $x^{2} - 3 k x + 2 k^{2} - 1 = 0$
is $7$ . The roots may be characterized as

Integral and positive

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Integral and negative

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Rational but not integral

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Irrational

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Imaginary

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Solution

The correct option is A Irrational
The product of the roots, here, is equal to $2 k^{2} - 1$ .
$∴ 2 k^{2} - 1 = 7, k^{2} = 4$ .
The discriminant $= (- 3 k)^{2} - 4 \cdot 1 \cdot (2 k^{2} - 1) = k^{2} + 4 = 8$ ;
therefore the roots are irrational.

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