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Question

(A) Given the quadratic equation $ax^2 + bx + c = 0$.Let the roots of the equation be $\alpha$ and $\frac{1}{\alpha}$ because they are reciprocal to e

Vedclass · Accepted Answer

$a - c = 0$

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(A) Given the quadratic equation $ax^2 + bx + c = 0$.Let the roots of the equation be $\alpha$ and $\frac{1}{\alpha}$ because they are reciprocal to each other.According to the properties of quadratic equations,the product of the roots is given by the ratio of the constant term to the coefficient of $x^2$.Product of roots = $\alpha \cdot \frac{1}{\alpha} = \frac{c}{a}$.Since $\alpha \cdot \frac{1}{\alpha} = 1$,we have $1 = \frac{c}{a}$.This implies $a = c$,or $a - c = 0$.

If the roots of the equation $ax^2 + bx + c = 0$ are reciprocal to each other,then:

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