How do I solve this problem?
my precalculus homework has this problem: “
x5+x4-3x3-11x2-28x-60=0 hint:2i is a solution” Im not sure how to solve this
1 Expert Answer
A degree 5 polynomial has 5 roots. If 2i is a root, so is -2i, so two of the factors are (x+2i)(x-2i) = x2+4. We have two roots, we need to find the other three
- Divide x5 + x4 - 3x3 - 11x2 - 28x - 60 by (x2+4). The quotient will be x3 + x2 - 7x - 15.
- Apply the Rational Root Theorem to see if there is a rational root to x3 + x2 - 7x - 15. There is, x = 3. Divide x3 + x2 - 7x - 15 by (x-3). The quotient is x2 + 4x + 5.
- Use the Quadratic Formula to find the roots of x2 + 4x + 5. The answer is -2 ± i.
- The roots are ±2i, 3, -2 ± i
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