SOLUTION: I am having trouble with a question, It is find the illegal values of c in the multiplication statement <PRE> c^2-3c-10 c^2-c-2 --------- * ---------- c^2+5c-14 c^2-2c-15

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: I am having trouble with a question, It is find the illegal values of c in the multiplication statement <PRE> c^2-3c-10 c^2-c-2 --------- * ---------- c^2+5c-14 c^2-2c-15      Log On


   

Question 6289: I am having trouble with a question, It is find the illegal values of c in the multiplication statement
c^2-3c-10    c^2-c-2
--------- * ----------
c^2+5c-14    c^2-2c-15

I think the answer is
c=-7, c=-3, c=2, and c=5
Am I right, Can someone let me know?
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
the illegal values is the values that make the two denominators equal to zero.
c^2+5c-14=0
c^2-2c-15=0
Solve both:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 1c%5E2%2B5c%2B-14+=+0) has the following solutons:

c%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=%285%29%5E2-4%2A1%2A-14=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+81+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%285%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+2
c%5B2%5D+=+%28-%285%29-sqrt%28+81+%29%29%2F2%5C1+=+-7

Quadratic expression 1c%5E2%2B5c%2B-14 can be factored:
1c%5E2%2B5c%2B-14+=+1%28c-2%29%2A%28c--7%29
Again, the answer is: 2, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-14+%29

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 1c%5E2%2B-2c%2B-15+=+0) has the following solutons:

c%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%2A-15=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+5
c%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C1+=+-3

Quadratic expression 1c%5E2%2B-2c%2B-15 can be factored:
1c%5E2%2B-2c%2B-15+=+1%28c-5%29%2A%28c--3%29
Again, the answer is: 5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-15+%29


So, the illegal values are 2, -7, 5, -3, you are right. Good job!