Question

I’ve been stuck on this problem for hours please help : college alg

Answer 1

P(x) = 4(x − (3 + 4i))(x − (3 − 4i))(x + 7)

Explanation:

The polynomial P of degree 3 with real coefficients will be of the form:

`P(x) = a(x - b)(x - c)(x - d)`

If a complex number is a root of a polynomial then its complex will be the root of that polynomial as well. Therefore,

`P(x) = a(x - (3 + 4i))(x - (3 - 4i))(x - (-7))`

Substitute the point (0, 700):

`700 = a(0 - (3 + 4i))(0 - (3 - 4i))(0 - (-7))\\700 = a(3 + 4i)(3 - 4i)(7)\\700 = a(3^2 - (4i)^2)(7)\\700 = a(3^2 + 4^2)(7)\\700 = a(9 + 16)(7)\\700 = a(25)(7)\\700 = 175a\\a = (700)/(175) = 4`

Now we can write the polynomial

`P(x)=4(x - (3 + 4i))(x - (3 - 4i))(x+7)`