How do you find the roots for #49x^2-14x-3#?

1 Answer
Apr 4, 2018

Answer:

#- 1/7, and 3/7#

Explanation:

Use the new Transforming Method (Socratic, Google Search):
#y = 49x^2 - 14x - 3 = 0#
Transformed equation:
#y' = x^2 - 14x - 147 = 0#
Method: Find 2 real roots of y', then, divide them by a = 49.
Find 2 real roots of y', that have opposite signs, knowing their sum (-b = 14) and their product (ac = - 147). They are -7, and 21.
The 2 real roots of y are:
#x1 = -7/a = -7/49 = - 1/7#, and #x2 = 21/49 = 3/7#