if -4 is the root of a quadratic equation x2+px-4=0 and the quadratic equation x2+px+k=0 has equal roots, find the value of k

Question

if -4 is the root of a quadratic equation x²+px-4=0 and the quadratic equation x²+px+k=0 has equal roots, find the value of k

Answer 1

Since -4 is a root, (-4)² + p(-4) - 4 = 0

 

                                      -4p +12 = 0   

 

                                             -4p = -12   So, p = 3

 

Therefore, x² + 3x + k = 0

 

Since there are equal roots, the discriminant = 0.  Recall that the discriminant of Ax²+Bx+C = 0 is B²-4AC.

 

So, 3² - 4(1)(k) = 0

 

           9 - 4k = 0    

 

             -4k = -9          Therefore, k = 9/4