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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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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
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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 = 47 = 3 (confirm) Thus Answer 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, 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 => (x4)(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 ProjectIf 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 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! 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 (X4)(X+7) = 0. other solution is X = 7. ANswer "A"



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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 (x4)(x+......) we also have x2 + 3x + k = 10, 4 + 7=3 so (x4)(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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18 Apr 2016, 11:48
solving for 4 to find k 16+12+k=10 k=18 (x^2)+3x18=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)(x4) = 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]
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27 Jan 2018, 06:11
put 4 in equation and solve for k So that gives k = 18 put it back in equation and solve for roots. one will come as 4 and another as 7.



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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
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27 Jan 2018, 07:09
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
Let's first determine the value of k. Since x = 4 is a solution to the equation x² + 3x + k = 10, we know that x = 4 SATISFIES the equation. That is: 4² + 3( 4) + k = 10 Evaluate to get: 16 + 12 + k = 10 Solve for k to get: k = 18So, the ORIGINAL equation is x² + 3x + ( 18) = 10 This is the same as: x² + 3x  18 = 10 We now need to solve this equation. First, set it equal to zero: x² + 3x  28 = 0 Factor: (x + 7)(x  4) = 0 So, x = 7 or x = 4 We already know that x = 4 is one solution. So, the other solution is x = 7 Answer: A Cheers, Brent
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
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27 Jan 2018, 07:46
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 \(k = 10  ( x^2 + 3x )\) Now, \(k = 10  ( 16 + 12 )\) Or, \(k = 18\) Put the value of k as 18 in the equation and solve now \(x^2 + 3x  18 = 10\) \(x^2 + 3x  28 = 0\) Actual solving the equation is not required, we already have one value as 4 , so the other value must be 7 ( As 28 = 4*7), Answer must be (A)
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]
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21 Feb 2018, 09:15
Bunuel wrote: 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: \(x^2 + 3x +(k10) =0\) 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. Hi Bunuel :) , i understand how you soled it, but regardimg Vieta`s properties \(x_1+x_2=\frac{b}{a}\) AND \(x_1*x_2=\frac{c}{a}\) how can i use these properties to find roots for example of this equation \(x^2+16x+64 =0\) if i follow the first property \(x_1+x_2=\frac{b}{a}\) i get \(x_1+x_2 = \frac{64}{1}\) the same question to the second property ... on the other hand i know tis rule > w So 64 is our C term The numbers that can multiply to make 64 are +8 and +8 (8*8 = 64) 16 is our B term Now find the two factors of C that add up to your B term 8 and 8 Hence 8+8 = 16 Now plug in values I have chosen into factored equation (x+a) (x+b)= 0 (x+8) (x+8)= 0 Now solve for X by equating to 0 (x+8) =0  > x = 8 (x+8)= 0  >x =  8 But i dont understand how to use these properties to get the same values( 8; 8) \(x_1+x_2=\frac{b}{a}\) AND \(x_1*x_2=\frac{c}{a}\) I would appreciate your fantastic explanation




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