Question

Use the given zero to find all the zeros of the function.

Function                                                                 zero

f (x) = 2x^4 - x^3 + 7x^2 - 4x - 4                             2i

Answer 1

Step 1:

The polynomial function is .

The root of the function is

Since the polynomial has only real coefficients, then must the conjugate be also a root.

Thus must also be a root of the polynomial.

.

is a one of the root of the function .

Step 2:

.

Apply the long division method.

Divide the first term of the dividend by the first term of the divisor .

So, the first term of the quotient is . Multiply  by and subtract.

Divide the first term of the last row by first term of the divisor .

So,the second term of the quotient is . Multiply by and subtract.

Divide the first term of the last row by first term of the divisor .

So,the second term of the quotient is . Multiply by and subtract.

Quotient is

Remainder is

Step 3:

Thus, .

The zeros of the function are .

Solution :

The zeros of the function are .