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

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by Max@Math Revolution » Fri Jan 25, 2019 1:14 am

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[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
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If 2 roots of the equation x^2+px+q=0 are -3 and 2

by fskilnik@GMATH » Fri Jan 25, 2019 6:12 am
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Brent@GMATPrepNow » Fri Jan 25, 2019 6:39 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If 2 roots of the equation x² + px + q = 0 are -3 and 2, what is the value of p + q?

A. -5
B. -3
C. -1
D. 0
E. 1
GIVEN: the roots/solutions are x = -3 and x = 2
Notice that x = -3 and x = 2 are solutions to the equation (x + 3)(x - 2) = 0
If we expand and simplify the left side of the equation, we get: x² + x - 6 = 0
So, the equation x² + x - 6 = 0 has roots -3 and 2
Compare this to x² + px + q = 0 to see that p = 1 and q = -6

What is the value of p + q?
p + q = 1 + (-6) = -5

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Jan 27, 2019 5:08 pm
=>
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
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