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

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Math Revolution GMAT Instructor
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If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 25 Jan 2019, 02:33
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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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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 25 Jan 2019, 03:01
1
MathRevolution wrote:
[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 \(p + q?\)

\(A. -5\)
\(B. -3\)
\(C. -1\)
\(D. 0\)
\(E. 1\)


When roots are given, i prefer the back solving approach

(x+3) (x-2)
x^2 + x -6

p+q = 1-6 = -5

A
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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 25 Jan 2019, 03:22
MathRevolution wrote:
[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 \(p + q?\)

\(A. -5\)
\(B. -3\)
\(C. -1\)
\(D. 0\)
\(E. 1\)



eqn would be
x^2+x-6= 0
p=1 q=-6
p+q = 1-6; -5
IMO A
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If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 25 Jan 2019, 07:25
MathRevolution 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.
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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 25 Jan 2019, 07:50
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Top Contributor
MathRevolution wrote:
[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 \(p + q?\)

\(A. -5\)
\(B. -3\)
\(C. -1\)
\(D. 0\)
\(E. 1\)


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
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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value  [#permalink]

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New post 27 Jan 2019, 18:28
=>
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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Re: If 2 roots of the equation x^2+px+q=0 are -3 and 2, what is the value   [#permalink] 27 Jan 2019, 18:28
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