If 4 is one solution of the equation x2 + 3x + k = 10, where : GMAT Problem Solving (PS)
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# If 4 is one solution of the equation x2 + 3x + k = 10, where

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If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 01:57
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If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600
[Reveal] Spoiler: OA

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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 01:57
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SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 02:13
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Slove equation by putting x=4 as it is one of the solution.
u gets value of k=-18

now put k=-18 in the equation,u get eqn in the form of ax^2+bx+c=0. Solving it we get x=4 and x=-7

so other solution is -7.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 04:07
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Shortcut for the question-

The sum of roots of a equation is = -b/a = -3
One of the given roots is 4
Thus the other root has to be -7
Check = 4-7 = -3 (confirm)

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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 05:25
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Bunuel wrote:

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Since 4 is one of the solution, so it must satisfy the equation.
Putting 4 as value of x: 4^2 + 3*4 + k = 10 => k =-18
so the equations is
x^2 + 3x - 28 = 0

Solving this by factorization gives => (x-4)(x+7) = 0
So x = -7 is other solution.

Hence A
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Sep 2012, 09:28
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

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One sol. of equation is 4. therefor putting this as X in the equation and finout the constant K.
therefore K = -28.
so, equation can be rewritten as (X-4)(X+7) = 0.

other solution is X = -7.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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21 Sep 2012, 02:34
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SOLUTION

If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$: $$x_1+x_2=-\frac{b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

Rewrite the equation given: $$x^2 + 3x +(k-10) =0$$
Thus according to the first property $$4+x_2=-\frac{3}{1}$$ --> $$x_2=-7$$. As we can see we can find the value of $$x_2$$ even without finding the value of $$k$$.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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23 Oct 2013, 05:03
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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04 Dec 2014, 09:22
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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01 Mar 2015, 18:52
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You don't need to solve for K, we know that 4 is a solution so we already know one of the terms (x-4)(x+......) we also have x2 + 3x + k = 10, -4 + 7=3 so (x-4)(x+7):0 hence x: -7
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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17 Apr 2016, 21:04
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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18 Apr 2016, 11:48
solving for 4 to find k
16+12+k=10
k=-18
(x^2)+3x-18=10
testing values you find -7
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

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28 Apr 2016, 06:28
Bunuel wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

(A) -7
(B) -4
(C) -3
(D) 1
(E) 6

Practice Questions
Question: 45
Page: 158
Difficulty: 600

The phrase “4 is one solution of the equation” means that one value of x is 4. Thus, we first must plug 4 for x into the given equation to determine the value of k. So we have

4^2 + (3)(4) + k = 10

16 + 12 + k = 10

28 + k = 10

k = -18

Next we plug -18 into the given equation for k and then solve for x.

x^2 + 3x – 18 = 10

x^2 + 3x – 28 = 0

(x+7)(x-4) = 0

x = -7 or x = 4

Thus, -7 is the other solution. Answer A.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where   [#permalink] 28 Apr 2016, 06:28
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