y = -4x^3 + 15x^2 - 1.
First, we find a number that gives a zero when plugged into the cubic Eq.
This is normally done by trial and error. but the use of EXCEL Spread
sheet made the task a lot easier.
It determined that -1/4 gives the zero that we need:
y = -4(-1/4)^3 + 15(-1/4)^2 - 1,
= 4/64 + 15/16 - 1,
= 1/16 + 15/16 - 1,
= 16/16 - 1 = 1 - 1 = 0.
x = -1/4,
x + 1/4 = 0 = a factor of the cubic Eq,
We divide the cubic Eq by its' factor to get a quadratic Eq:
(-4x^3 + 15x^2 - 1)/ (x + 1/4) =
-4x^2 + 16x - 4.(Long hand division was used).
Eq2: y = -4x^2 + 16x - 4 = 0.
Divide both sides by -4 and get:
y = x^2 - 4x + 1 = 0,
Use the Quadratic Formula to find x:
x = (4 +- sqrt(16 - 4)) / 2,
= (4 +- sqrt(12)) / 2,
= (4 +- 3.464) / 2,
= 2 +- 1.732 = 3.732, and 0.268.
Solution set: (3.732 , 0) ,(0.268 , 0).
quadratic Eq
How would you solve this equation for x?
y= -4x^3+15x^2-1
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