Find a formula for the polynomial P(x) with degree 3 real coefficients zeros at x=-4 +3i and x=-3 y intercept at (0,75) P(x)=

Question

Find a formula for the polynomial  with

degree 3

real coefficients

zeros at x=-4 +3i and x=-3

y intercept at (0,75)

Answer 1

With imaginary or complex roots, they have to come in pairs. Thus, 2 solutions are:

x = -4 ± 3i

thus, the 2 factors are: x + 4 - 3i, and x + 4 + 3i

Multiplying these, we get:

x2 + 8x + 25

We are given x = -3, so the 3rd factor is x + 3. Multiply this by the equation above, and we have:

x³ + 11x² + 49x + 75

If x = 0, we have the specified value of 75