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GRE Quantitative Practice, Standard Multiple-Choice

Question 1

If x2 + 6x = –9, how many values of x are possible?

  1. none
  2. one
  3. two
  4. three
  5. infinitely many

Explanatory Answer

First, restate the equation in standard quadratic form:

x2 + 6x + 9 = 0
The trinomial on the left side of the equation is factorable into two identical binomials:
(x + 3)(x + 3) = 0

To find the roots, set each binomial factor equal to zero. Since the two factors are the same, the equation has only one root: –3. The correct response is (B).