SOLUTION: Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −1, 0, 4, 1/4 ; coefficient of x3 is 13

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −1, 0, 4, 1/4 ; coefficient of x3 is 13      Log On


   

Question 1008060: Find a polynomial of the specified degree that satisfies the given conditions.
Degree 4; zeros −1, 0, 4, 1/4 ; coefficient of x3 is 13
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Moving through one step ahead, 13x%28x%2B1%29%28x-4%29%28x-1%2F4%29. Multiply into general form if you want.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Degree 4;
zeros: x%5B1%5D=-1, x%5B2%5D=0,x%5B3%5D=+4,x%5B4%5D=+1%2F4
coefficient of x%5E3 is 13
f%28x%29=ax%5E4%2B13x%5E3%2Bcx%5E2%2Bdx%2Be
%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29=0
%28x%2B1%29%28x-0%29%28x-4%29%28x-1%2F4%29=0
%28x%5E2%2Bx%29%28x-4%29%28x-1%2F4%29=0
%28x%5E3%2Bx%5E2-4x%5E2-4x%29%28x-1%2F4%29=0
%28x%5E3-3x%5E2-4x%29%28x-1%2F4%29=0
x%5E4-3x%5E3-4x%5E2+++-%281%2F4%29x%5E3%2B3x%5E2%281%2F4%29%2B4%281%2F4%29x=0
x%5E4-3x%5E3+-x%5E3%2F4%2B3x%5E2%2F4-4x%5E2%2Bx=0
x%5E4-12x%5E3%2F4+-x%5E3%2F4%2B3x%5E2%2F4-16x%5E2%2F4%2Bx=0
x%5E4-13x%5E3%2F4+-13x%5E2%2F4%2Bx=0.....multiply all terms by 4
4x%5E4-4%2813x%5E3%29%2F4-4%2813x%5E2%29%2F4%2B4x=0
4x%5E4-13x%5E3-13x%5E2%2B4x=0
so, your polynomial is:
f%28x%29=4x%5E4-13x%5E3-13x%5E2%2B4x
+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C4x%5E4-13x%5E3-13x%5E2%2B4x%29+