SOLUTION: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, $f(1) = -5, and f(2) = 12, then what are the $x$-intercepts of the graph of f?

Question 1030147: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, $f(1) = -5, and f(2) = 12, then what are the $x$-intercepts of the graph of f?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let .
Since f(0)= 0, ==> d = 0
==>
Now f(-1) = 15 ==> -a + b - c = 15, while
f(1) = -5 ==> a + b + c = -5.
Adding the corresponding sides of the two preceding equations, we get b = 5.
==> a + c = -10 <--------Equation (A)
f(2) = 12 ==> 8a + 4b + 2c = 12 ==> 8a+20+2c = 12, or
4a+c = -4 <----------Equation (B)
after simplifying...
Solving for a and c from Equations A and B, we get a = 2 and c = -12.
==> .
The roots correspond to the x-coordinates of the x-intercepts. Thus the x-intercepts are (0,0), (3/2,0), and (-4,0).

RELATED QUESTIONS
The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then... (answered by stanbon)

The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then... (answered by Boreal,stanbon)

The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then... (answered by Fombitz)

The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then... (answered by greenestamps)

The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) =... (answered by ikleyn)

Please help me to solve those problems. I would really appreciate any help.Thanks!... (answered by robertb)

If f is a polynomial of degree 4 such that f(0) = f(1) = f(2) = f(3) = 1 and f(4) = 0, (answered by math_helper)

Pls help! If you can answer either one of them, I am so appreciated. 1.(x-2)(x+3)^2 /... (answered by Fombitz)