SOLUTION: Find the value of the following polynomial for the given values of the variable. Value #1: x = -3 Value #2: x = -2 -x^2 - 5x -6 ?

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Find the value of the following polynomial for the given values of the variable. Value #1: x = -3 Value #2: x = -2 -x^2 - 5x -6 ?      Log On

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Question 39573This question is from textbook Beginning Algebra
: Find the value of the following polynomial for the given values of the variable.
Value #1: x = -3
Value #2: x = -2
-x^2 - 5x -6 ?This question is from textbook Beginning Algebra

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Value #1: x = -3
-x%5E2+-+5x+-+6
-%28-3%29%5E2+-+5%28-3%29+-+6
-9+%2B+15+-+6
0
Value #2: x = -2
-%28-2%29%5E2+-+5%28-2%29+-+6
-4+%2B+10+-+6
0
If you look at the parabola below, the zeroes are at -3 and -2.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-5x%2B-6+=+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%2A-1%2A-6=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C-1+=+-3
x%5B2%5D+=+%28-%28-5%29-sqrt%28+1+%29%29%2F2%5C-1+=+-2

Quadratic expression -1x%5E2%2B-5x%2B-6 can be factored:
-1x%5E2%2B-5x%2B-6+=+-1%28x--3%29%2A%28x--2%29
Again, the answer is: -3, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-5%2Ax%2B-6+%29