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 ->  Rational-functions -> 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 1131317: 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(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given zeros:
x%5B1%5D=3,
x%5B2%5D=-13, and
x%5B3%5D=5+%2B+4i-> complex roots always come in pairs, so you 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+%2B4i%29
f%28x%29=%28x%5E2+%2B+10+x+-+39%29%28x%5E2+-+10+x+%2B+41%29
f%28x%29=x%5E4+-+98+x%5E2+%2B+800+x+-+1599