Question

Find an Nth degree polynomial function with real coefficients satisfying the given conditions. Write answer in standard form. N=4, zeros: -2,1, and 3i, also f(-3)=144

Standard form:

Answer 1

f(x) = 2x⁴ + 26x² + 72

Step-by-step explanation:

Imaginary and complex roots come in conjugate pairs. So if 2i and 3i are zeros, then -2i and -3i are also zeros.

f(x) = a (x − 2i) (x + 2i) (x − 3i) (x + 3i)

f(x) = a (x² − 4i²) (x² − 9i²)

f(x) = a (x² + 4) (x² + 9)

f(x) = a (x⁴ + 13x² + 36)

f(-1) = 100

100 = a ((-1)⁴ + 13(-1)² + 36)

100 = a (1 + 13 + 36)

100 = 50a

a = 2

f(x) = 2 (x⁴ + 13x² + 36)

f(x) = 2x⁴ + 26x² + 72

Step-by-step explanation: