How do you solve x^2 + 6x - 7 = 0x2+6x−7=0?

1 Answer
George C.
Jul 7, 2015

Notice x=1x=1 is a root since the sum of the coefficients is 00.
Then find the other root x=-7x=−7

Explanation:

Let f(x) = x^2+6x-7f(x)=x2+6x−7

First notice that the sum of the coefficients is zero: 1 + 6 - 7 = 01+6−7=0
so f(1) = 0f(1)=0, 11 is a root and (x-1)(x−1) is a factor of f(x)f(x).

In order to get the x^2x2 leading term and -7−7 constant term, the other factor must be (x+7)(x+7), giving the other root as x = -7x=−7

x^2+6x-7 = (x-1)(x+7)x2+6x−7=(x−1)(x+7)

Related questions
See all questions in Comparing Methods for Solving Quadratics
Impact of this question
10854 views around the world
You can reuse this answer
Creative Commons License