# A quadratic equation whose diffrence of roots is 3 and the sum of the square of the roots is 29 is given by

Answers (1)

Solution:

$\\ \left | \alpha -\beta \right |=3;and;\alpha ^2+\beta ^2=29\\ \\\Rightarrow \left | \alpha -\beta \right |^2=9\\ \\\Rightarrow \alpha ^2+\beta ^2-2\alpha \beta =9\\ \\\Rightarrow \alpha \beta =10\\ \\\Rightarrow (\alpha +\beta )^2=\alpha ^2+\beta ^2+2\alpha \beta \Rightarrow (\alpha +\beta )=\pm 7$

Requried equation is$\\x^2\pm 7x+10=0$

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