MathRevolution wrote:

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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.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)

Our high-level "quant" preparation starts here: https://gmath.net