SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i

Algebra ->  Real-numbers -> SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i       Log On


   

Question 1129075: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given roots:
x%5B1%5D=3
x%5B2%5D=+-13 and
x%5B3%5D=5+%2B+4i => recall that complex roots always come in pairs; so, you will also have
x%5B4%5D=5-+4i

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-3%29%28x-%28-13%29%29%28x-%285+%2B+4i%29%29%28x-%285-+4i%29%29
f%28x%29=%28x-3%29%28x%2B13%29%28x-5+-+4i%29%28x-5%2B+4i%29
f%28x%29=%28x%5E2%2B13x-3x-39%29%28x%5E2-5x%2B+4xi-5x%2B25-20i-4xi%2B20i-16i%5E2%29
f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25-16%28-1%29%29
f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B25%2B16%29
f%28x%29=%28x%5E2%2B10x-39%29%28x%5E2-10x%2B41%29
f%28x%29=x%5E4+-+98x%5E2+%2B+800x+-+1599