Question

if -1 is a zero of the quadratic polynomial,p(x)= kx^2-5x-4,then find the value of k

Answer 1

0=k*(-1)^2-5(-1)-4
0=k+5-4
k=-1

Answer 2

If  α  is a root (or zero) of the polynomial  p(x) = k x² - 5 x - 4 
then,    p(x = α) = 0.

Given -1 is a zero of p(x).
 So  p(x = -1) = 0
       k (-1)² - 5 (-1) - 4 = 0
       k + 5 - 4 = 0
       k = -1.