Question

find the quadratic equation for which the sum iof the roots is 1 and the sum of of squares of the roots is 13​

Answer 1

Let the roots be α and β

According to question..........

sum of roots = 1

α + β= 1

sum of square of roots = 13

$\alpha ^{2} + \beta ^{2} = 13$

NOW,

$(\alpha +\beta)^{2} = \alpha^{2} + \beta^{2} + 2\alpha \beta \\\\(1)^{2} = 13 + 2\alpha \beta \\\\2\alpha \beta = -12\\\\\alpha \beta = -6$

Now, we know that the equation is in the form of :---

$x^{2} - (\alpha +\beta )x +(\alpha \beta ) = 0$

So, put the values in this equation.....

$x^{2} - (1)x + (-6) = 0\\\\x^{2} - x - 6 = 0$