SOLUTION: (-a2square+3a-2)(a2square+3a-2) How do I solve this problem?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (-a2square+3a-2)(a2square+3a-2) How do I solve this problem?      Log On


   



Question 661407: (-a2square+3a-2)(a2square+3a-2)
How do I solve this problem?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29+ ...set it equal to zero and solve for a

%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29=0+...here you have the product of two polynomial, and that product will e equal to zero if either one or both of them is equal to zero
so, take this factor %28-a%5E2%2B3a-2%29=0+ and find a that makes it equal to zero
%28-a%5E2%2B3a-2%29=0+...use quadratic formula..(don't be confused with unknown variable labeled with a, same as a coefficient -1)
a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A%28-2%29+%29%29%2F%282%2A%28-1%29%29+

a+=+%28-3+%2B-+sqrt%28+9-8+%29%29%2F-2+
a+=+%28-3+%2B-+sqrt%28+1+%29%29%2F-2+
a+=+%28-3+%2B-+1%29%2F-2+
solutions:
a+=+%28-3+%2B+1%29%2F-2+
a+=+-2%2F-2+
highlight%28a+=+1%29+

a+=+%28-3+-1%29%2F-2+
a+=+-4%2F-2+
highlight%28a+=+2%29+

now, do the same with second factor in given product

a%5E2%2B3a-2=0+

a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29%29+

a+=+%28-3+%2B-+sqrt%289%2B8+%29%29%2F2+

a+=+%28-3+%2B-+sqrt%2817+%29%29%2F2+

a+=+%28-3+%2B-+4.12%29%29%2F2+

solutions:

a+=+%28-3+%2B4.12%29%2F2+

a+=+1.12%2F2+
highlight%28a+=+0.56%29+

a+=+%28-3+-4.12%29%2F2+

a+=+-7.12%2F2+

highlight%28a+=+-3.56%29+

so, there are four solutions because, if you multiply given polynomials you will get polynomial of fourth degree -a%5E4%2B9a%5E2-12a%2B4

+graph%28600%2C+600%2C+-5%2C+5%2C+-5%2C+55%2C+-x%5E4%2B9x%5E2-12x%2B4%29+