SOLUTION: Write the equation, in standard form, of a polynomial with real coefficients that has roots at 2, 1−2i, and 1+4i, and passes through the point (0,98). Your answer should

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Write the equation, in standard form, of a polynomial with real coefficients that has roots at 2, 1−2i, and 1+4i, and passes through the point (0,98). Your answer should       Log On


   

Question 930626: Write the equation, in standard form, of a polynomial with real coefficients that has roots at 2, 1−2i, and 1+4i, and passes through the point (0,98).
Your answer should include only (decimal) numbers, the letter "x", and the characters "+", "-", and "^"
f(x)=___________
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation, in standard form, of a polynomial with real coefficients that has roots at :
2,
1-2i, complex roots always come in pairs, so you have 1%2B2i too
1%2B4i, and 1-4i as well
passes through the point (0,98).
where a is coefficient
f%28x%29=a%28x%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%29
since passes through the point (0,98) set f%28x%29=98 and x=0 and solve for coefficient a

98=a%280%5E5-6%2A0%5E4%2B34%2A0%5E3-96%2A0%5E2%2B173%2A0-170%29
98=a%28-170%29
a=98%2F%28-170%29
a=-0.5764705882352941 exact value, and for more accurate result I will use exact value
f%28x%29=-0.5764705882352941%28x%5E5-6x%5E4%2B34x%5E3-96x%5E2%2B173x-170%29


we can round it and get shorter form, but zeros will not be exact
f%28x%29=-0.58x%5E5%2B3.46x%5E4-19.6x%5E3%2B55.34x%5E2-99.7x%2B98