Answer:
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
