fskilnik wrote:

GMATH practice exercise (Quant Class 14)

If the polynomial \(p\) in the variable \(x\) is defined by \(\,p\left( x \right) = k{x^2} - kx - 12\), for all values of \(x\), what is the value of the constant \(k\) ?

(1) \(p\left( 3 \right) = 0\)

(2) The polynomial \(p\) is divisible by \(x+2\)

Obs.: although the above version of the question stem is a bit "wordy", we believe it´s better (mathematically speaking).

\(p\left( x \right) = k{x^2} - kx - 12\,\,\,\,\,\left( * \right)\)

\(? = k\)

\(\left( 1 \right)\,\,\,0\,\, = \,\,p\left( 3 \right)\,\,\mathop = \limits^{\left( * \right)} \,\,k{\left( 3 \right)^2} - k\left( 3 \right) - 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\)

\(\left( 2 \right)\,\,\,0 = p\left( { - 2} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,k{\left( { - 2} \right)^2} - k\left( { - 2} \right) - 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}\)

The correct answer is therefore (D).

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