If -1 is a zero of the quadratic polynomial,p(x)= kx²-5x-4,then find the value of k
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.
To find the value of k, we will use the fact that -1 is a zero of the quadratic polynomial p(x).
When -1 is a zero of p(x), it means that p(-1) = 0.
Substituting -1 into the polynomial p(x), we get:
p(-1) = k(-1)² - 5(-1) - 4
Simplifying this expression:
p(-1) = k + 5 - 4
p(-1) = k + 1
Since p(-1) = 0, we can set this equation equal to zero:
k + 1 = 0
Subtracting 1 from both sides:
k = -1
Therefore, the value of k is -1.