Asked by Mary
Form a polynomial, f(x) with real coefficients having the given degree and zeros. Degree: 4 ; Zeros: 4i and 5i
Really need help! don't know where to start.
Really need help! don't know where to start.
Answers
Answered by
Steve
Review the properties of polynomials with real coefficients. If they have complex roots, the roots appear in conjugate pairs. So, since you have roots 4i and 5i, the other roots are -4i and -5i.
Recall that x^2 + a^2 = (x-ai)(x+ai)
So, your polynomial is (x^2+16)(x^2+25) = x^4 + 41x^2 + 400
Recall that x^2 + a^2 = (x-ai)(x+ai)
So, your polynomial is (x^2+16)(x^2+25) = x^4 + 41x^2 + 400