SOLUTION: Given the zero: x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others.

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Given the zero: x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 430003: Given the zero: x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others.
Found 3 solutions by poliphob3.14, ewatrrr, htmentor:
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:%28x%5E3-4x%5E2%2B21x-34%29%2F%28x-2%29=x%5E2-2x%2B17
Find the roots of x%5E2-2x%2B17=0
x=%282%2B-sqrt%28-64%29%29%2F2, x=1+4i and x=1-4i.
Answer: The zeros of polynomial are:2, 1+4i, 1-4i.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

 Given the zero: x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others.



 x^3-4x^2+21x-34 = (x-2)(x^2 - 2x + 17)

 x^2 - 2x + 17 = 0    |Using standard form: ax^2+bx +c = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

x+=+%282+%2B-+sqrt%28+-64+%29%29%2F%282%29+

 x+=+%282+%2B-+8i%29%2F%282%29+ 

    x = 1 + 4i

and x = 1 - 4i

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
We are given x = 2 is one of the zeros, so we know that x - 2 is one of the factors of the polynomial
We can divide the polynomial by x - 2 to get a quadratic:
x^3-4x^2+21x-34/x-2
Performing the division gives x%5E2+-+2x+%2B+17
Now use the quadratic formula to get the other two zeros:
x+=+%282+%2B-+sqrt%284+-+68%29%29%2F2
The other two roots are complex, and are equal to:
x = 1 + 4i, and x = 1 - 4i