Question

-4 is a root of the quadratic Equation x^2 + kx-4=0 and the quadratic Equation x^2+px+k=0 find the value of p and k

Answer 1

let
p(x)=x²+kx-4 & q(x)=x²+px+k,

since -4 is a root of both the quadratic equations then
p(-4) and q(-4) both should be equal to zero.

then

p(-4)=0,

(-4)²+k(-4)-4=0,

16-4k-4=0,

12=4k,

then

k=3,

also
q(-4)=0,

(-4)²+p(-4)+3=0,

16-4p+3=0,

then

19=4p,

p=19/4