Question

How do you solve `(10x + 3) ( 3x^{2} - 11x - 4) = 0`?

Answer 1

`-3/10, 1/3, and -4`

Explanation:

`f(x) = (10x + 3)(3x^2 - 11x - 4) = 0`
a. (10x + 3) = 0 --> `x = - 3/10`
b. Solve the quadratic equation by the new Transforming Method (Socratic Search):
`y = 3x^2 - 11x - 4 = 0`
Transformed equation `y' = x^2 - 11x - 12 = 0`
Since a + b + c = 0, use shortcut. The 2 real roots of y' are: 1 and
`c/a = - 12`. Divide them by a = 3 to get the 2 real roots of y.
They are: `x1 = 1/3` and `x2 = -12/3 = -4`.
Answers:
`-3/10, 1/3 and -4`