Question

How do you solve `4x^2 - 17x - 15 = 0` by factoring?

Answer 1

Solve `f(x) = 4x^2 - 17x - 15 = 0`

Ans: `-3/4` and 5

Explanation:

I use the new Transforming Method (Socratic Search).
Transformed equation: `f(x)' = x^2 - 17x - 60`. (2) Roots have opposite signs. Factor pairs of (-60) --> (-2, 30)(-3, 20). This sum is 17 = -b. Then, the 2 real roots of (2) are: y1 = -3 and y2 = 20.
Back to original equation, the 2 real roots are: `x1 = (y1)/a = -3/4` and `x2 = (y2)/a = 20/4 = 5`.