Question

What is a polynomial function in standard form with zeroes 1, 2, –3, and –3?


g(x) = x^4 + 3x^3 –7x^2 – 15x + 18
g(x) = x^4 + 3x^3 –7x^2 + 2x + 18
g(x) = x^4 – 3x^3 + 7x^2 + 15x + 18
g(x) = x^4 – 3x^3 –7x^2 + 15x + 18

Answer 1

For any polynomial equation with real coefficients, complex roots occur in conjugate pairs.
So, if 5i i.e. (0 + 5i) is a root then (0 - 5i) is the other root.
Hence, the 4 zeros are x = -1, 2, 5i, - 5i

Answer 2

sorry thats all iknow

Answer 3

Hint:
g(x) = (x - 1)(x - 2)(x + 3)^2

Answer 4

The roots give you the factored form of the function. Each root is where the function equals zero, so set the factored form equal to zero:
\[(x-1)(x-2)(x+3)(x+3)=0\]By expandign this you can approach one of your multiple choice answers