SOLUTION: Write a polynomial with rational coefficients so that P(x)=0 has the given roots: -1 and -2i?
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Question 1005610: Write a polynomial with rational coefficients so that P(x)=0 has the given roots: -1 and -2i?
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
roots are -1 and +/- 2i, because complex roots are conjugate. This is a cubic equation.
the factors are (x+1) and (x^2+4), since x^2+4=0, and the roots are +/- 2i
the polynomial is x^3+x^2+4x+4=f(x)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
has the given roots:
and
if we have then we also have because complex roots always come in pairs
use zero product formula
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