Quadratic equation with one of the roots as a part of equationIf α,β are roots of x2−4α+1=0, then equation whose roots are 14−α,14−β is?

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Charlie Haley · Accepted Answer

Given:&amp;nbsp;x2−4α+1=0Now we write something as&amp;nbsp;()2−4α+1=0.Inside the bracket we write such an expression of x such that substituting&amp;nbsp;x=14−α&amp;nbsp;in that expression leaves us only with&amp;nbsp;α&amp;nbsp;and our uppermost equation gets satisfied. Such an expression is&amp;nbsp;1−1x+4. Therefore our required equation is&amp;nbsp;(1−1x+4)2−4α+1=0You may now simplify itNote: We didn&#039;t discussed about another root&amp;nbsp;14−β&amp;nbsp;as it s similar looking to&amp;nbsp;14−α. Therefore if our equation works for one it works for other as well.

Quadratic equation with one of the roots as

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