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

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

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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.

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
21 Sep 2012, 02:34

1

This post received KUDOS

Expert's post

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 \(k\).

Answer: A.

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

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

Hello from the GMAT Club BumpBot!

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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
01 Mar 2015, 18:52

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

gmatclubot

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where
[#permalink]
01 Mar 2015, 18:52

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