Question

For what value of k is -2 a zero of the polynomial f(x) = x(2 - 3x) + k?

Answer 1

Hint: The zero or root of a polynomial is the point at which the value of the polynomial is zero, or we can say that the graph of the polynomial touches the x-axis. To find the value of k, we will substitute -2 in the equation and equate it to zero.

Complete step-by-step answer:

We have been given that-

f(x) = x(2 - 3x) + k

If -2 is a zero of f(x) then-

f(-2) = 0

f(-2) = (-2)(2 - 3(-2)) + k = 0

f(-2) = (-2)(2 + 6) +k = 0

k -16 = 0

k = 16

Hence, when the value of k is 16, then -2 is a zero or a root of the polynomial f(x). This is the required answer.

Note: Students may get confused in the language of the question. One common mistake is that they substitute x = 0 and equate the polynomial with -2 to find the value of k, which is incorrect. It is recommended that we verify the answer by substituting the obtained value of k and then finding the value of f(-2).