MathRevolution wrote:

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Math Revolution GMAT math practice question]

Does \(x^2+px+q = 0\) have a root?

\(1) p<0\)

\(2) q<0\)

\(?\,\,\,:\,\,\,\,\Delta = \left( {{\text{}}{b^2} - 4ac{\text{}}} \right) = {p^2} - 4q\,\,\,\mathop \geqslant \limits^? \,\,\,\,0\,\,\)

\(\left( 1 \right)\,\,\,\left\{ \begin{gathered}

\,Take\,\,\left( {p,q} \right) = \left( { - 1,0} \right)\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\

\,Take\,\,\left( {p,q} \right) = \left( { - 1,1} \right)\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\

\end{gathered} \right.\)

\(\left( 2 \right)\,\,\,q < 0\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS!}}} \,\,\, - 4q > 0\,\,\,\,\mathop \Rightarrow \limits^{{{\text{p}}^{\text{2}}}\,\, \geqslant \,\,0} \,\,\,{p^2} - 4q > 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle\)

Conclusion: the correct answer is (B).

The above follows the notations and rationale taught in the GMATH method.

_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)

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