Question

The sum of two roots of a quadratic equation is 5 and sum of their square is 35 , find the equation

Answer 1

Given that :-

$\alpha + \beta = 5 \\ \\ now \\ \\ { \alpha }^{2} + { \beta }^{2} = 35 \\ \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = 35 \\ \\ {5}^{2} - 2 \alpha \beta = 35 \\ \\ 2 \alpha \beta = 25 - 35 = ( - 10) \\ \\ \alpha \beta = \frac{ - 10}{2} = ( - 5) \\ \\ \\ \\ now \\ \\ the \: general \: form \: of \: quadratic \: equation \: is \: \\ \\ k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ \\ \\ putting \: the \: values \\ \\ k( {x}^{2} - 5x - 5) \\ \\ \\ for \: k = 1 \\ \\ p(x) = {x}^{2} - 5x - 5$


Thus

The equation is

P(x) = x²-5x-5