Question

if the sum of the roots is -p and product of the roots is 1/p then the quadratic polynomial is​

Answer 1

Answer:

$\rm px^2 +p^2x +1 =0$

Step-by-step explanation:

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

$\rm x^2 -(-p)x +\dfrac{1}{p} =0$

$\rm x^2 +px +\dfrac{1}{p} =0$

Multiply both sides by p,

$\rm p(x^2 +px +\dfrac{1}{p}) =p×0$

$\rm px^2 +p^2x +1 =0$