SOLUTION: Use the given zero to find the remailning zeros of the function. f(x)= x^3-3x^2-5x+39; zero: -3 Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the given zero to find the remailning zeros of the function. f(x)= x^3-3x^2-5x+39; zero: -3 Thank you      Log On


   

Question 284698: Use the given zero to find the remailning zeros of the function.
f(x)= x^3-3x^2-5x+39; zero: -3
Thank you
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
if x=-3 then x+3 is a factor.
divide the equation by (x+3) and get x^2-6 x+13
which has two complex roots
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B13+=+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=%28-6%29%5E2-4%2A1%2A13=-16.

The discriminant -16 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 -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28--6%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28--6%2B-+i%2A4%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-6%2Ax%2B13+%29