Problem Solving

[Math Revolution GMAT math practice question]

If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value of p + q?

A. -5
B. -3
C. -1
D. 0
E. 1

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If the 2 roots of the equation x^2+px+q=0 are -3 and 2, where p and q are constants, what is the value of p + q?

A. -5
B. -3
C. -1
D. 0
E. 1

$$? = p + q$$
$$\left\{ \matrix{
\, - 1 = - 3 + 2 = {\rm{sum}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\, - p \hfill \cr
\, - 6 = - 3 \cdot 2 = {\rm{product}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,q \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = p + q = 1 + \left( { - 6} \right) = - 5$$
$$\left( * \right)\,\,\,\left\{ \matrix{
a{x^2} + bx + c = 0\,\,,\,\,\,a \ne {\rm{0}} \hfill \cr
\Delta \ge 0\,\,\,,\,\,\,{\rm{roots}}\,\,{x_1}\,\,{\rm{and}}\,\,{x_2} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,{x_1} + {x_2} = - {b \over a} \hfill \cr
\,{x_1} \cdot {x_2} = {c \over a} \hfill \cr} \right.$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

=>
The equation of this form with roots -3 and 2 is (x+3)(x-2) = 0 or x^2 + x - 6 = 0.
Thus, p = 1 and q = -6, and
p + q = -5.
Therefore, the answer is A.
Answer: A