If alpha and beta are the roots of the equati | vedclass

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(B) Given the equation $x^2 + px + q = 0$ with roots $\alpha$ and $\beta$.We know that $\alpha + \beta = -p$ and $\alpha \beta = q$.Let the new roots

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$x^2 + px + q = 0$

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(B) Given the equation $x^2 + px + q = 0$ with roots $\alpha$ and $\beta$.We know that $\alpha + \beta = -p$ and $\alpha \beta = q$.Let the new roots be $\alpha' = q/\alpha$ and $\beta' = q/\beta$.The sum of the new roots is $\alpha' + \beta' = \frac{q}{\alpha} + \frac{q}{\beta} = q \left( \frac{\alpha + \beta}{\alpha \beta} ight) = q \left( \frac{-p}{q} ight) = -p$.The product of the new roots is $\alpha' \beta' = \left( \frac{q}{\alpha} ight) \left( \frac{q}{\beta} ight) = \frac{q^2}{\alpha \beta} = \frac{q^2}{q} = q$.The required equation is $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^2 - (-p)x + q = 0$,which simplifies to $x^2 + px + q = 0$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + px + q = 0$,then what is the equation whose roots are $q/\alpha$ and $q/\beta$?

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