Question

If -4 is a root of the quadratic equation $x^2-px-4=0$ and the quadratic equation $x^2-px+k=0$ has equal roots, then the value of k is:

Answer 1

$x^2-px-4=0$

sum of roots $\Rightarrow -4+A=\frac{-b}{a}$

$\Rightarrow -4+A=\frac{p}{1}$

$\Rightarrow -4+A=p$ __ (1)

Product of roots $\Rightarrow (-4)\left(A\right)=\frac{c}{a}$

$\Rightarrow -4\left(A\right)=-4$

$\Rightarrow A=1$

Put A = 1 in eq. (1)

$-4+1=p$

$\therefore p=-3$

$x^2-px+K=0$

$x^2+3x+K=0$

If roots are equal, D=0

$D=b^2-4ac$

$O=3^2-4K$

$4K=9$

$K=\frac{9}{4}$