Question

The sum of roots of quadratic equation is 5 and the sum of squares is 13 find the equation

Answer 1

Answer:

the equation when taken x as a variable is

$x {}^{2} - 5x + 6$

Solution,

let a and b be the roots of the required equation,

therefore a+b=5 (given)

and

$a {}^{2} + b {}^{2} = 13$

now

$(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

$a {}^{2} + b {}^{2} = (a + b) {}^{2} - 2ab$

$13 = (5) {}^{2} { - 2ab}$

$12 = 2ab \\ ab = 6$

now the required equation is

$x {}^{2} - (sum \: of \: the \: roots)x \\ + (product \: of \: the \: roots)$

$x {}^{2} - 5x + 6$

is the equation