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

1 Answer
Sep 30, 2015

Answer:

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#.