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Question

(A) For a quadratic equation of the form $ax^2 + bx + c = 0$,if the roots are reciprocals of each other,then their product is equal to $1$.Let the roo

Vedclass · Accepted Answer

$5$

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(A) For a quadratic equation of the form $ax^2 + bx + c = 0$,if the roots are reciprocals of each other,then their product is equal to $1$.Let the roots be $\alpha$ and $1/\alpha$.The product of the roots is given by the formula $\frac{c}{a}$.Here,$a = 5$,$b = -7$,and $c = k$.Therefore,$\alpha \cdot \frac{1}{\alpha} = \frac{k}{5}$.$1 = \frac{k}{5}$.Multiplying both sides by $5$,we get $k = 5$.

If the roots of the equation $5x^2 - 7x + k = 0$ are reciprocals of each other,then the value of $k$ is:

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