Question
If -1 is a zero of the quadratic polynomial,p(x)= kx²-5x-4,then find the value of k
Answers
Answered by
GPT 3.5
If -1 is a zero of the quadratic polynomial p(x) = kx² - 5x - 4, it means that when we substitute x = -1 into the polynomial, the result will be 0.
So let's substitute x = -1 into the polynomial:
p(x) = kx² - 5x - 4
p(-1) = k(-1)² - 5(-1) - 4
p(-1) = k + 5 - 4
p(-1) = k + 1
Since we know that p(-1) = 0, we can set k + 1 equal to zero:
k + 1 = 0
k = -1
Therefore, the value of k is -1.
So let's substitute x = -1 into the polynomial:
p(x) = kx² - 5x - 4
p(-1) = k(-1)² - 5(-1) - 4
p(-1) = k + 5 - 4
p(-1) = k + 1
Since we know that p(-1) = 0, we can set k + 1 equal to zero:
k + 1 = 0
k = -1
Therefore, the value of k is -1.