SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2-i

Algebra.Com
Question 1127284: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2-i
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!


MUST be degree 4.
Zero being means that another zero is .

Do the multiplications if you want "simplified".
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

For any polynomial with real coefficients, the roots go in pairs (complex number, conjugate complex number).


Therefore, at given condition, the roots of the polynomial are  -2, 2-i  and 2+i,

and one possible polynomial is THIS


    f(x) = (x+2)*(x-(2-i))*(x-(2+i)), which is the same as


    f(x) = (x+2)*((x-2)+i)*((x-2)-i) = (x+2)*((x-2)^2+1).


For your safety,  ignore the post by  @josgarithmetic, since it is   W R O N G,   as usual.



RELATED QUESTIONS

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -3,... (answered by aaronwiz)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -2, 2 (answered by jsmallt9)
Find a polynomial f(x) of degree 4 with real coefficients and the following zeros... (answered by ikleyn)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.... (answered by solver91311)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros -4,1-i (answered by hkwu)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros -4,1-i (answered by hkwu)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: 4, 2... (answered by solver91311)
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: -2,... (answered by nerdybill)
Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1,... (answered by MathLover1)