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If and are the roots of the equation {x}^{2}-px+q=0, then fi

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If $α$ and $β$ are the roots of the equation $x^{2} - p x + q = 0,$ then find the equation whose roots are $\frac{q}{p - α}$ and $\frac{q}{p - β}$

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α

and

β

are the roots of the equation

x^{2} - p x + q = 0,

then find the equation whose roots are

\frac{q}{p - α}

and

\frac{q}{p - β}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let

\frac{q}{p - α} = x

\Rightarrow α = p - \frac{q}{x}

So, we replace

x

p - \frac{q}{x}

in the equation, we get

(p - \frac{q}{x})^{2} - p (p - \frac{q}{x}) + q = 0

\Rightarrow p^{2} + \frac{q ^{2}}{x ^{2}} - \frac{2 pq}{x} - p^{2} + \frac{pq}{x} + q = 0

\Rightarrow \frac{q}{x ^{2}} - \frac{p}{x} + 1 = 0

\Rightarrow x^{2} - p x + q = 0

is the required equation whose roots are

\frac{q}{p - α}

and

\frac{q}{p - β}

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Question Text	If $α$ and $β$ are the roots of the equation $x^{2} - p x + q = 0,$ then find the equation whose roots are $\frac{q}{p - α}$ and $\frac{q}{p - β}$
Answer Type	Text solution:1
Upvotes	150