Question

if - 4 is a root of quadratic equation x^2 + px + k = 0 and the quadratic equation x^2 + px + k =0 has equal roots find the value of k

not able to find the answer anywhere. somebody , ​

Answer 1

$\bold\blue{Question}$

If -4 is a root of quadratic equation $\bold{x^{2}+px+k=0}$ and the quadratic equation has equal roots find the value of k.

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{The \ value \ of \ k \ is \ 16.}$

$\bold\blue{Explanation}$

The given quadratic equation is

$\bold{x^{2}+px+k=0.}$

Here,a=1, b=p and c=k.

$\bold{Product \ of \ roots=\frac{c}{a}}$

$\bold\orange{Given:}$

The given quadratic equation is

$\bold{x^{2}+px+k=0.}$

-4 is one of the root.

Equation has equal roots.

$\bold\pink{To \ find:}$

The value of k.

$\bold\green{\underline{\underline{Solution}}}$

The given quadratic equation is

$\bold{x^{2}+px+k=0.}$

The equation has equal roots, therefore other root will also be -4.

We know,

$\bold{Product \ of \ roots=\frac{c}{a}}$

$\bold{-4×(-4)=\frac{k}{1}}$

$\bold{k=16}$

Therefore,

$\bold\purple{The \ value \ of \ k \ is \ 16.}$