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).
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