SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -8, and 2 + 5i

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. 4, -8, and 2 + 5i       Log On


   



Question 1125277: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -8, and 2 + 5i

Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2-5i is another root, because complex roots come as conjugates.
factors are (x-4)(x+8) and x-2-5i and x-2+5i
The first two multiply to x^2+4x-32
The last two are x^2-4x+29
The polynomial is 4th degree
x^4-19x^2+244x-928
graph%28300%2C300%2C-10%2C10%2C-1200%2C500%2Cx%5E4-19x%5E2%2B244x-928%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given zeros:
x%5B1%5D=4, x%5B2%5D=-8, and x%5B3%5D=2+%2B+5i+
since you have 2+%2B+5i+, you also have x%5B4%5D=2+-+5i+ because complex zeros come always in pairs

so, your unction has four zeros, and it will be a polynomial function of fourth degree
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-4%29%28x-%28-8%29%29%28x-%282+%2B+5i%29%29%28x-%282+-+5i%29%29

f%28x%29=%28x-4%29%28x%2B8%29%28x-2+-+5i%29%29%28x-2+%2B5i%29%29

f%28x%29=%28x%5E2-4x%2B8x-32%29%28x%5E2-2x%2B5xi-2x%2B4-10i-5xi%2B10i-25i%5E2+%29

f%28x%29=%28x%5E2%2B4x-32%29%28x%5E2-4x+%2B4-25%28-1%29+%29

f%28x%29=%28x%5E2%2B4x-32%29%28x%5E2-4x+%2B4%2B25+%29

f%28x%29=%28x%5E2%2B4x-32%29%28x%5E2-4x+%2B29+%29

f%28x%29=x%5E4+-+19+x%5E2+%2B+244+x+-+928