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Question

If one zero of 2x2-3x+k is reciprocal to the other, then find the value of k.


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Solution

Find the value of k.

Given: One zero of 2x2-3x+k is reciprocal to the other.

let α be the one root of the quadratic equation.

So, the other root will be 1α.

We know that for the quadratic equation ax2+bx+c product of the roots is given by ca.

Thus, the product of the roots of given quadratic equation =k2.

α×1α=k22=kk=2

Hence, the value of k is 2.


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