Question

Find $p$ in the equation $x^2-4x+p=0$, if it is known that the sum of the squares of its roots is equal to $16$.

Answer 1

The equation is $x^2-4x+p=0$

let the roots are $x_{1}and{x}_2$

and it is given that $x_1^2+x_2^2=16$

product of the root is =$\frac{4}{1}$

$x_1\times x_2=4$

the sum of the roots is $=\frac{p}{1}$

$x_1+x_2=p$

know we have,

$(x_1+x_2{)}^2=x_1^2+x_2^2+2\times x_1\times x_2$

$(p{)}^2=16+2\times 4$

$p^2=24$

$p=\sqrt{24}$

$p=2\sqrt{6}$ answer.