SOLUTION: Write a polynomial function with the rational coefficent,s so that P(x)=0 has the given roots. 2, 3, 5 -1 , -1, 1

Algebra ->  Rational-functions -> SOLUTION: Write a polynomial function with the rational coefficent,s so that P(x)=0 has the given roots. 2, 3, 5 -1 , -1, 1      Log On


   

Question 696158: Write a polynomial function with the rational coefficent,s so that P(x)=0 has the given roots.
2, 3, 5
-1 , -1, 1
Found 2 solutions by mouk, MathLover1:
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
If P(x) has a root a then (x-a) is a factor.
So 2, 3, 5: +P%28x%29=%28x-2%29%28x-3%29%28x-5%29+
and -1 , -1, 1: +P%28x%29=%28x%2B1%29%28x%2B1%29%28x-1%29+=+%28x%2B1%29%5E2%28x-1%29+

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
P%28x%29=0 has the given roots:
x%5B1%5D=2 and y%5B1%5D=-1
x%5B2%5D=+3 and y%5B2%5D=+-1
+x%5B3%5D=5 and +y%5B3%5D=1

%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29=0
%28x-2%29%28x-3%29%28x-5%29=0...........multiply
%28x%5E2-3x-2x%2B6%29%28x-5%29=0
x%5E3-5x%5E2-3x%5E2%2B15x-2x%5E2%2B10x%2B6x-30=0
x%5E3-10x%5E2%2B31x-30=0

+graph%28+600%2C+600%2C+-10%2C+10%2C+-35%2C10%2Cgrid%281%29%2Cx%5E3-10x%5E2%2B31x-30%29+