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If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 06:06
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If \(f(x) = 5x^2  4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ? A. 10 B. 5 C. 0 D. 5 E. 10 Kudos for a correct solution.
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 06:06
SOLUTIONIf \(f(x) = 5x^2  4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ?A. 10 B. 5 C. 0 D. 5 E. 10 \(f(x) = 5x^2  4\), then \(f(m  1)=5(m1)^2  4=5m^210 m+1\); \(g(x) = 3x + 1\), then \(g(m^2 + 1)=3(m^2 + 1) + 1=3m^2+4\). Since given that \(f(m  1) = g(m^2 + 1)\), then \(5m^210 m+1=3m^2+4\) > \(2m^210m3=0\). Next, Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):
\(x_1+x_2=\frac{b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).Thus according to the above \(m_1+m_2=\frac{(10)}{2}=5\). Answer: D. Try NEW Algebra DS question.
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 08:46
F(x)=5x^24 F(m1)=5(m1)^24 5(m^22m+1)4 5m^210m+54 5m^210m+1
G(x)=3x+1 G(m^2+1)=3(m^2+1)+1 3m^2+3+1 3m^2+4
5m^210m+1=3m^2+4 2m^210m3=0
D=b^24ac D=1004(6)=100+24=124
x(1) = 10+2(root)31/4 x(2) = 102(root)31/4
10+2(root)31/4 + 102(root)31/4 = 20/4 = 5
Answer is D



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 08:53
The ans is 5
putting the values gives us 2m^210m3=0
solving this gives us m= (10+sqrt(124))/4 and (10sqrt(124))/4
21/41/4 =5 ans



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 10:19
Bunuel wrote: If \(f(x) = 5x^2  4\)and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ? A. 10 B. 5 C. 0 D. 5 E. 10 Kudos for a correct solution. f(m1)= 5(m1)^2 4 = 5(m^2+12m) 4 =5m^2+510m4 = 5m^210m +1 g(m^2+1)= 3(m^2+1) +1 =3m^2+4 now f(m1)=g(m^2+1) 5m^210m +1 = 3m^2+4 2m^210m 3=0 also, any quadratic equation can be written as x^2(sum of the roots)x + product of the roots here since coeff. of m^2 is 2, therefore we will divide the whole expression by 2 and we will get, m^25m3/2=0 thus sum of roots = 5 hence D



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 12:11
Substituting (m1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,
5(m1)^24=3(m^2+1) 5m^210m+54=3m^2+3+1 2m^210m=0 2m(m5)=0
2m=0 and m5=0
The roots of m are 0 and 5 and their sum is 5
Answer D



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 18:33
Subbing (m1) into f(x) yields 5m^2  10m + 1
Subbing (m^2 + 1) into g(x) yields 3m^2 + 4
Setting f(m1) equal to g(m^2 + 1) yields 3m^2 + 1 = 5m^2  10m + 1
This simplifies to 0 = 2m^2  10m  3
Using Viete's rules, we know that the sum of the roots x1 and x2 in ax^2 + bx + c is equal to b/a, hence x1 + x2 = (10)/2 = 5
This is the desired answer. Therefore, D.



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 22:42
\(f(x) = 5x^2  4\) \(f(m1) = 5 (m1)^2  4\) \(= 5(m^2  2m + 1)  4\) \(= 5m^2  10m + 5  4\) \(= 5m^2  10m + 1\) .............. (1) g(x) = 3x+1 \(g(m^2 + 1) = 3(m^2 + 1) + 1\) \(= 3m^2 + 4\) ............ (2) Equating (1) & (2) \(5m^2  10m + 1 = 3m^2 + 4\) \(2m^2  10m  3 = 0\) Sum of roots \(= \frac{(10)}{2} = 5\) Answer = D
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Jul 2014, 22:46
fra wrote: Substituting (m1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,
5(m1)^24=3(m^2+1) 5m^210m+54=3m^2+3+1 2m^210m=0 2m(m5)=0
2m=0 and m5=0
The roots of m are 0 and 5 and their sum is 5
Answer D Equation would come up as \(2m^2  10m  3\) Answer = D, however individual roots cannot be 0 & 5
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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10 Jul 2014, 00:37
Thanks for pointing that out!



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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15 Jul 2014, 10:31
SOLUTIONIf \(f(x) = 5x^2  4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ?A. 10 B. 5 C. 0 D. 5 E. 10 \(f(x) = 5x^2  4\), then \(f(m  1)=5(m1)^2  4=5m^210 m+1\); \(g(x) = 3x + 1\), then \(g(m^2 + 1)=3(m^2 + 1) + 1=3m^2+4\). Since given that \(f(m  1) = g(m^2 + 1)\), then \(5m^210 m+1=3m^2+4\) > \(2m^210m3=0\). Next, Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):
\(x_1+x_2=\frac{b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).Thus according to the above \(m_1+m_2=\frac{(10)}{2}=5\). Answer: D. Kudos points given to correct solutions.Try NEW Algebra DS question.
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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17 Apr 2015, 05:21
If \(f(x) = 5x^2  4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ? A. 10 B. 5 C. 0 D. 5 E. 10 Kudos for a correct solution. [/quote] f(m1) = g(m^2+1) 5(m1)^24=3(m^2+1)+1 2m^2  10m  3 = 0 Sum of roots is = b/a so 10/2 = 5
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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11 May 2016, 02:47
f(m1) = g(m^2+1) 5(m1)^24=3(m^2+1)+1 2m^2  10m  3 = 0 For equation aX^2+bX+C=0 sum of roots =(b/a)
so here sum of roots= (10/2) = 5



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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09 Apr 2017, 02:05
Bunuel wrote: If \(f(x) = 5x^2  4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m  1) = g(m^2 + 1)\) ? A. 10 B. 5 C. 0 D. 5 E. 10 Kudos for a correct solution. Pleas find attached the solution. My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam. Posted from my mobile device
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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10 Apr 2017, 02:11
GMATinsight wrote: Pleas find attached the solution.
My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam.
Dear GMATInsight, I'd like to draw you attention that there is an error in f(x) function. You have changed it from (4) to (+4). The final quadratic equation should be: 2m^2  10m  3 = 0



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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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10 Apr 2017, 03:18
Mo2men wrote: GMATinsight wrote: Pleas find attached the solution.
My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam.
Dear GMATInsight, I'd like to draw you attention that there is an error in f(x) function. You have changed it from (4) to (+4). The final quadratic equation should be: 2m^2  10m  3 = 0 Thanks for notifying my mistake... However the pleasant surprise is that answer still doesn't change as the answer is dependent on the coefficients of x^2 and x... So I hope that is ok if I accept the mistake made in first step however endorse the method to find answer (roots) of a quadratic equation.
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
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