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 find k?

Answer 1

Since one root is given of the first equation,
We put that root x=-4 ,
thus p= 3.
Now putting the value of p in equation (ii)
We get
X^2 + 3X + k = 0
According to question , Equation has equal roots
So, b^2 -4ac = 0
thus k = 9/4.

Answer 2

Given,-4 is the root of the equation X^2+pX+-4=0 .
so,p(-4)=(-4)^2-4p-4=0
=16-4p-4=0
p=3
substituting p in the next equation,
x^2+3x+k=0.
it has equal roots,so b^2-4ac=0
3^2-4×1×k=0
k=9/4