SOLUTION: Use the given zero to find the remaining zeros of the function. h(x)=4x^4+7x^3+34x^2+63x-18; zero; -3i. Please show work.

Question 1002792: Use the given zero to find the remaining zeros of the function. h(x)=4x^4+7x^3+34x^2+63x-18; zero; -3i. Please show work.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If a polynomial has a complex zero, then the conjugate of that zero is also a zero of the polynomial. Since

is a zero,

must also be a zero.

If

is a zero of a polynomial, then

is a factor of the polynomial. Hence,

and

are both factors of the given function.

Multiply these two factors (Hint: The product of two conjugates is the difference of two squares, but since

you will get the sum of two squares.

Use Polynomial Long Division to divide the above product into the original function. Since the divisor is quadratic and the dividend is quartic, the quotient will be quadratic and, therefore, solvable by any convenient means. Hint: it factors, but the quadratic formula is quicker.

If you need a refresher on Polynomial Long Division, see: Purple Math Polynomial Long Division. Note that the divisor is a quadratic with no linear term, so you will need a placeholder in the divisor.

John

My calculator said it, I believe it, that settles it

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