SOLUTION: Given a zero x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others. Did I do this right? x(x^2-4x+21)-34=0 x(x-7)(x+3)-34=0 x= -7 x= -3 If I am off base, can you s

Algebra ->  Rational-functions -> SOLUTION: Given a zero x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others. Did I do this right? x(x^2-4x+21)-34=0 x(x-7)(x+3)-34=0 x= -7 x= -3 If I am off base, can you s      Log On


   

Question 205193: Given a zero x=2, of the polynomial: x^3-4x^2+21x-34=0, find the others.
Did I do this right?
x(x^2-4x+21)-34=0
x(x-7)(x+3)-34=0
x= -7 x= -3
If I am off base, can you show the correct way to do this problem? Thank you
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x-2=0 since 2 is a zero.
(x^3-4x^2+21x-34)/(x-2) Long division
=x^2-2x+17
x^2-2x+17=0
x=1+4i, x=1-4i The other 2 zeros. Quadratic formula (see below)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B17+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A17=-64.

The discriminant -64 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -64 is + or - sqrt%28+64%29+=+8.

The solution is x%5B12%5D+=+%28--2%2B-+i%2Asqrt%28+-64+%29%29%2F2%5C1+=++%28--2%2B-+i%2A8%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B17+%29