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# In the equation x^2 + bx + 12 = 0, x is a variable and b is

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In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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29 Jan 2014, 02:14
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
(2) 4 is a root of the equation x^2 + bx + 12 = 0.

Data Sufficiency
Question: 62
Category: Algebra First- and second-degree equations
Page: 157
Difficulty: 600

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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29 Jan 2014, 02:15
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SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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29 Jan 2014, 02:51
From S1:x-3 is a factor of the given equation=>x=3 is a root of the equation.Putting x=3 in the eq x^2+bx+12 we can get the value of b.Hence sufficient.
From S2:4 is a root of the equation=>Putting x=4 in the equation we can find out b.Sufficient.
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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01 Feb 2014, 09:45
SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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09 Sep 2016, 22:01
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

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16 Jul 2017, 13:25
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In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1)$$x - 3$$ is a factor of $$x^2 + bx + 12$$

as $$(x-3)$$ is one of the factor, this means that $$x = 3$$ is one of the roots of the equation $$x^2 + bx + 12$$

In order to get 12 = we only have one value after 3 and that is 4 as $$4 * 3 = 12$$

Hence, $$bx = 4x + 3x = 7x$$, value of $$b = 7$$

Hence, (1) ===== is SUFFICIENT

(2) 4 is a root of the equation $$x^2 + bx + 12 = 0$$

As 4 is one of the roots, the other root will be 3

Hence, $$bx = 4x + 3x = 7x$$, value of $$b = 7$$

Hence, (2) ===== is SUFFICIENT

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is   [#permalink] 16 Jul 2017, 13:25
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