Find the quadratic equation whose roots are r | vedclass

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(A) The given quadratic equation is $3x^{2}-20x+17=0$.If the roots of the equation $ax^{2}+bx+c=0$ are $\alpha$ and $\beta$,then the equation whose ro

Vedclass · Accepted Answer

$17x^{2}-20x+3=0$

Vedclass · Answer

(A) The given quadratic equation is $3x^{2}-20x+17=0$.If the roots of the equation $ax^{2}+bx+c=0$ are $\alpha$ and $\beta$,then the equation whose roots are $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is obtained by replacing $x$ with $\frac{1}{x}$.Substituting $x = \frac{1}{x}$ in the given equation:$3(\frac{1}{x})^{2}-20(\frac{1}{x})+17=0$$\frac{3}{x^{2}}-\frac{20}{x}+17=0$Multiplying the entire equation by $x^{2}$:$3-20x+17x^{2}=0$Rearranging the terms,we get:$17x^{2}-20x+3=0$.

Find the quadratic equation whose roots are reciprocals of the roots of the equation $3x^{2}-20x+17=0$.

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