SOLUTION: Given that one zero is 9, find the other zeros for this polynomial fucntion: {{{f(x)=x^3-14x^2+47x-18}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Given that one zero is 9, find the other zeros for this polynomial fucntion: {{{f(x)=x^3-14x^2+47x-18}}}      Log On


   

Question 122575: Given that one zero is 9, find the other zeros for this polynomial fucntion:
f%28x%29=x%5E3-14x%5E2%2B47x-18
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x^3-14x^2+47x-18
x^3-14x^2+47x-18/x-9=x^2-5x+2 Long division.
x^2-5x+2=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B2+=+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=%28-5%29%5E2-4%2A1%2A2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+4.56155281280883
x%5B2%5D+=+%28-%28-5%29-sqrt%28+17+%29%29%2F2%5C1+=+0.43844718719117

Quadratic expression 1x%5E2%2B-5x%2B2 can be factored:
1x%5E2%2B-5x%2B2+=+%28x-4.56155281280883%29%2A%28x-0.43844718719117%29
Again, the answer is: 4.56155281280883, 0.43844718719117. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B2+%29