Question

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

Answer 1

x² + p x + k = 0  has equal roots.
So discriminant    p² - 4 k = 0    => k = p²/4

Substitute this value in the 1st equation.

                                      x² + p x  - 4 - p²/4  = 0
Since -4 is a root :         16 - 4 p - 4 - p²/4  =0 

=>                               p² + 16 p - 48 = 0
=>                          p = - 8  + 4√7      or  8 - 4 √7

=>          k = p²/4 = (48 - 16 p) / 4 
               k  = 44  - 16√7    or   44 + 16 √7

Answer 2

plz refer to this attachment