SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 5, -3, and -1 + 2i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 5, -3, and -1 + 2i      Log On


   



Question 1127540: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
5, -3, and -1 + 2i

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
x%5B1%5D=5,
x%5B2%5D=-3
and
x%5B3%5D=-1+%2B+2i=> complex roots come in pairs, so you also have x%5B4%5D=-1+-+2i
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-5%29%28x-%28-3%29%29%28x-%28-1+%2B+2i%29%29%28x-%28-1+-+2i%29%29
f%28x%29=%28x-5%29%28x%2B3%29%28x%2B1+-2i%29%28x%2B1%2B+2i%29
f%28x%29=%28x%5E2-2x-15%29%28x%5E2+%2B+2x+%2B+5%29
f%28x%29=x%5E4+%2B+2x%5E3+%2B+5x%5E2-2x%5E3-4x%5E2-10x-15x%5E2-30x-75
f%28x%29=x%5E4+%2B+cross%282x%5E3%29+%2B+5x%5E2-cross%282x%5E3%29-19x%5E2-40x-75
f%28x%29=x%5E4-14x%5E2-40x-75