SOLUTION: write the polynomial function with the given roots. 1.2,1,-2 2.5,1,4,-1 3.1/2,1/3,-1,1 4.6,1,3,-1 5.-1,0,1,3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: write the polynomial function with the given roots. 1.2,1,-2 2.5,1,4,-1 3.1/2,1/3,-1,1 4.6,1,3,-1 5.-1,0,1,3      Log On


   

Question 911795: write the polynomial function with the given roots.
1.2,1,-2
2.5,1,4,-1
3.1/2,1/3,-1,1
4.6,1,3,-1
5.-1,0,1,3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do just the longest one.  You do the others the same way:

1%2F2,1%2F3,-1,1

Set x equal to each:

x=1%2F2,x=1%2F3,x=-1,x=1

Get 0 on the right of each by subtracting the number on
the right of each from both sides of each

x-1%2F2=0,x-1%2F3=0,x%2B1=0,x-1=0

Clear the equations of fractions that have fractions:

2x-1=0,3x-1=0,x%2B1=0,x-1=0

Put all those left sides in parentheses:

%282x-1%29=0,%283x-1%29=0,%28x%2B1%29=0,%28x-1%29=0

Multiply equals by equals 4 times:

%282x-1%29%283x-1%29%28x%2B1%29%28x-1%29=0

FOIL the first two and then FOIL the last two:

%286x%5E2-5x%2B1%29%28x%5E2-1%29=0

Multiply every term in the first parentheses by every term in
the second parentheses:

6x%5E4-6x%5E2-5x%5E3%2B5x%2Bx%5E2-1=0

Collect like terms

6x%5E4-5x%5E3-5x%5E2%2B5x-1=0

Do the others the exact same way.

Edwin