find the zeros of f(x), ans state the multiplicity of each zero in order.

Question

Find the zeros of f(x), and state the multiplicity of each zero. (Order your answers from smallest to largest x first by real part, then by imaginary part.)

f(x) = x⁴ + 16x² − 225

zero______ Multiplicity______

zero______ Multiplicity______

zero______ Multiplicity______

zero______ Multiplicity______

Answer 1

I used the graphing calculator to see the the real zeros are x=3 and x=-3 Each have a multiplicity of 1.

I used synthetic division to find the others.

3 | 1 0 16 0 -225

3 9 75 225

-3 | 1 3 25 75 0 (The zero at the end confirms there is no remainder and this is a factor)

-3 0 -75

1 0 25 0 (The zero at the end confirms there is no remainder and this is a factor)

The factor that remains is x²+25

Set this factor equal to zero and solve

x²+25=0 Subtract 25 from both sides

x²=-25 Take the square root of both sides

x=5i and x=-5i Each have a multiplicity of 1.