SOLUTION: Someone please help me with this. I highly appreciate. find a polynomial of degree 4 that has zeros -3, 0, 1, and 5; and the coefficient of x^3 is -3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Someone please help me with this. I highly appreciate. find a polynomial of degree 4 that has zeros -3, 0, 1, and 5; and the coefficient of x^3 is -3      Log On


   

Question 953893: Someone please help me with this. I highly appreciate. find a polynomial of degree 4 that has zeros -3, 0, 1, and 5; and the coefficient of x^3 is -3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a polynomial of degree 4 that has zeros x%5B1%5D=-3, x%5B2%5D=0, x%5B3%5D=1, and x%5B4%5D=5;

use zero product rule:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x%2B3%29%28x-0%29%28x-1%29%28x-5%29
f%28x%29=%28x%2B3%29%28x%29%28x-1%29%28x-5%29
f%28x%29=%28x%5E2%2B3x%29%28x%5E2-5x-x%2B5%29
f%28x%29=%28x%5E2%2B3x%29%28x%5E2-6x%2B5%29
f%28x%29=x%5E4-6x%5E3%2B5x%5E2%2B3x%5E3-18x%5E2%2B15x
f%28x%29=x%5E4-3x%5E3-13x%5E2%2B15x

+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C+x%5E4-3x%5E3-13x%5E2%2B15x%29+