SOLUTION: Help Solve please. I am so confused!! Multiply.[a + 1/5][a+1/4] Thank you for your help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Help Solve please. I am so confused!! Multiply.[a + 1/5][a+1/4] Thank you for your help.      Log On


   

Question 150432: Help Solve please. I am so confused!!
Multiply.[a + 1/5][a+1/4]
Thank you for your help.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Multiplying,
%28a%2B1%2F5%29%28a%2B1%2F4%29
a%5E2+%281%2F5%29a%2B%281%2F4%29a+1%2F20
a%5E2+%284a%2B5a%29%2F20+1%2F20
a%5E2+9a%2F20+1%2F20 -----> your answer when multiplied.
To get "a", by quadratic eqn: a=1,b=9%2F20,c=+1%2F20
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation a0%5E2%2Bb0%2Bc=0 (in our case 10%5E2%2B0.450%2B0.05+=+0) has the following solutons:

0%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=%280.45%29%5E2-4%2A1%2A0.05=0.0025.

Discriminant d=0.0025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.45%2B-sqrt%28+0.0025+%29%29%2F2%5Ca.

0%5B1%5D+=+%28-%280.45%29%2Bsqrt%28+0.0025+%29%29%2F2%5C1+=+-0.2
0%5B2%5D+=+%28-%280.45%29-sqrt%28+0.0025+%29%29%2F2%5C1+=+-0.25

Quadratic expression 10%5E2%2B0.450%2B0.05 can be factored:
10%5E2%2B0.450%2B0.05+=+1%280--0.2%29%2A%280--0.25%29
Again, the answer is: -0.2, -0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0.45%2Ax%2B0.05+%29