Answer:
The zeros of given polynomial are: 0, 2 and 3
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 2x^4 - 9x^3 + 7x^2 + 6x[/tex]
We have to find the zeroes of the given polynomial.
We can say that the zeroes of a polynomial are defined as the points where the polynomial equals to zero.
[tex]f(-3) = 2(-3)^4 - 9(-3)^3 + 7(-3)^2 + 6(-3) = 450\\f(-2) = 2(-2)^4 - 9(-2)^3 + 7(-2)^2 + 6(-2) = 120\\f(-1) = 2(-1)^4 - 9(-1)^3 + 7(-1)^2 + 6(-1) = 12\\f(0) = 2(0)^4 - 9(0)^3 + 7(0)^2 + 6(0) = 0\\f(1) = 2(1)^4 - 9(1)^3 + 7(1)^2 + 6(1) = 6\\f(2) = 2(2)^4 - 9(2)^3 + 7(2)^2 + 6(2) =0\\f(3) = 2(3)^4 - 9(3)^3 + 7(3)^2 + 6(3) = 0[/tex]
Hence, the zeros of given polynomial are: 0, 2 and 3
