SOLUTION: Hello, I need help in solving the following problem, I have tried but I do not understand how to solve the problem. Here the problem: Solve {{{t^4-11t^2+18}}} Tha

Algebra ->  Equations -> SOLUTION: Hello, I need help in solving the following problem, I have tried but I do not understand how to solve the problem. Here the problem: Solve {{{t^4-11t^2+18}}} Tha      Log On


   

Question 246717: Hello,
I need help in solving the following problem, I have tried but I do not understand how to solve the problem.
Here the problem:

Solve t%5E4-11t%5E2%2B18


Thank you so much, I think that you guys are great to help people like me, I been out of school for 15 years and it hard trying to remember how to solve these type of problems.

Found 2 solutions by nerdybill, richwmiller:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
I assume they are asking you to factor it.
.
t%5E4-11t%5E2%2B18
%28t%5E2-9%29%28t%5E2-2%29
%28t-3%29%28t%2B3%29%28t%5E2-2%29
You could leave it like that or, you could factor the last term as:
%28t-3%29%28t%2B3%29%28t-sqrt%282%29%29%28t%2Bsqrt%282%29%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We are going to use a little trick to solve this.
Substitute u for t^2
That gives us
u^2-11+18=0
we can solve with the factoring, quadratic formula or complete the square
factoring is the easiest
(u-2)(-9)=0
u=2
u=9
but u=x^2 so
+\- means plus or minus
+\-t=sqrt(u)
so we have four solutions
t=+\-sqrt(2)
t=+\-3
see below to use the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-11x%2B18+=+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=%28-11%29%5E2-4%2A1%2A18=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-11%29-sqrt%28+49+%29%29%2F2%5C1+=+2

Quadratic expression 1x%5E2%2B-11x%2B18 can be factored:
1x%5E2%2B-11x%2B18+=+1%28x-9%29%2A%28x-2%29
Again, the answer is: 9, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B18+%29