Thread: Need help solving a cubic function for a, b, c, and d

I need to solve for a, b, c, and d for a cubic equation with points (2,24), (-2,0), (0,0), and (3,0). I plugged them into the equation getting these equations:
8a + 4b + 2c + d = 24
-8a + 4b + -2c + d = 0
27a + 9b + 3c = 0
d = 0

I put the numbers into a matrix and tried to solve with Gaussian elimination but I couldn't get rid of the 27 without a huge mess. I don't know any other way to do it. Please help.

Originally Posted by mono1357

I need to solve for a, b, c, and d for a cubic equation with points (2,24), (-2,0), (0,0), and (3,0). I plugged them into the equation getting these equations:
8a + 4b + 2c + d = 24
-8a + 4b + -2c + d = 0
27a + 9b + 3c = 0
d = 0

I put the numbers into a matrix and tried to solve with Gaussian elimination but I couldn't get rid of the 27 without a huge mess. I don't know any other way to do it. Please help.

Have you done the obvious things? Substitute d = 0, divide equations through by common factors ..... You get:

4a + 2b + c = 12 .... (1)

-4a + 2b - c = 0 .... (2)

9a + 3b + c = 0 .... (3)

(1) + (2) => b = 3.

Now substitute b = 3 and solve for a and c .....