SOLUTION: can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i
Algebra.Com
Question 86425: can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i
:
First factor is easy:
x = 3
1st factor is: (x-3)= 0
:
x = 3 + i
Think of it as the reverse of completing the square
x - 3 = i
Square both sides
(x-3)^2 = i^2;
x^2 - 6x + 9 = -1: FOILed (x-3(x-3); we know that i^2 = -1
x^2 - 6x + 9 + 1 = 0
x^2 - 6x + 10 = 0; is the 2nd factor
:
Multiply the two factors the long way:
(x-3) * (x^2 - 6x + 10) = x^3 - 9x^2 + 28x - 30 is the polynomial
:
Did this help?
RELATED QUESTIONS
Find a polynomial with integer coefficients that satisfies the given conditions.
Q has... (answered by edjones)
Find a polynomial with integer coefficients that satisfies the given conditions.
Q has... (answered by CubeyThePenguin)
Find a polynomial with integer coefficients that satisfies the given conditions.
Q has... (answered by Boreal,Edwin McCravy)
I need help with this: find a polynomial with integer coefficients that has the given... (answered by venugopalramana)
Find a polynomial with integer coefficients taht satisfies the given conditions. Q has... (answered by Alan3354,jsmallt9)
I can't figure out even where to start with this question, could you walk me through... (answered by stanbon)
Find a polynomial with integer coefficients that satisfies the given conditions.
P has... (answered by Fombitz)
Find a polynomial with integer coefficients that satisfies the given conditions.
Q(X)... (answered by edjones)
find a polynomial function of smallest degree with integer coefficients that has the... (answered by Alan3354)