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By what factor should the smaller root of the equation 6x^2 -13x + 6 =

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By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 31 May 2019, 09:29
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By what factor should the smaller root of the equation 6x^2 -13x + 6 = 0 increase so that it equals larger root of the equation.


A. 4/9
B. 5/6
C. 6/5
D. 2
E. 9/4
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 31 May 2019, 12:20
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 02:29
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 04:20
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4


Hi, I wanted to ask
if I do it this way
2/3+x = 3/2
x gives 5/6 (b) in that case

Why don't we add in order to increase it ? and multiply instead ?
What part of language I missed ?
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By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 04:29
2
1
quote="Luca1111111111111"]
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?[/quote]

Luca1111111111111
Hi there, no trick at all
I used to find it challenging at once

its like normal quadratic only, the 6 with X^2 leads to confusion for some

here is how you can do it-
In the equation
aX^2 + bX + c = 0
a= 6 and c = 6 as you can see
we have to multiply these roots
as you already know,
AC multiplied is what the product of the equation is, and b is the sum of roots (which is -13 here)
for AC = 36,
there is 9 and 4 which multiplied gives 36, and will give us the sum of 9+4=13, but we don't need +13 here

also -9 and -4 will give the same result, 36, and will give us -13 too, the sum we need. voila!

Therefore the equation can be written as
6x^2-13x+6 = 0
6x^2 - 9x - 4x +6 = 0
now take common factors out
3x(2x-3) -2 (2x-3) = 0
(3x-2) = 0 and (2x-3) = 0
x = 3/2 and 2/3
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 04:43
kiran120680 wrote:
By what factor should the smaller root of the equation 6x^2 -13x + 6 = 0 increase so that it equals larger root of the equation.


A. 4/9
B. 5/6
C. 6/5
D. 2
E. 9/4

Solve the quadratic equation to find:

x= 3/2 and 2/3
Larger root = k * Smaller root, to find k
3/2 = k* (2/3)
9/4 = k
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 04:47
1
Shrey9 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4


Hi, I wanted to ask
if I do it this way
2/3+x = 3/2
x gives 5/6 (b) in that case

Why don't we add in order to increase it ? and multiply instead ?
What part of language I missed ?

Shrey9
Increase/reduce by a factor means multiplied/divided.

GMAT also plays with words like increase to and increase by...
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 06:06
Shrey9 wrote:
quote="Luca1111111111111"]
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?


Luca1111111111111
Hi there, no trick at all
I used to find it challenging at once

its like normal quadratic only, the 6 with X^2 leads to confusion for some

here is how you can do it-
In the equation
aX^2 + bX + c = 0
a= 6 and c = 6 as you can see
we have to multiply these roots
as you already know,
AC multiplied is what the product of the equation is, and b is the sum of roots (which is -13 here)
for AC = 36,
there is 9 and 4 which multiplied gives 36, and will give us the sum of 9+4=13, but we don't need +13 here

also -9 and -4 will give the same result, 36, and will give us -13 too, the sum we need. voila!

Therefore the equation can be written as
6x^2-13x+6 = 0
6x^2 - 9x - 4x +6 = 0
now take common factors out
3x(2x-3) -2 (2x-3) = 0
(3x-2) = 0 and (2x-3) = 0
x = 3/2 and 2/3[/quote]

Thank you so much!!
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 09:07
1
Luca1111111111111 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?


Yes there certainly is a formula for solving this , \(x\) = \(\frac{-b \pm \sqrt{b^2-4ac}}{2a}\) if \(b^2>4ac\)
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =  [#permalink]

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New post 02 Jun 2019, 13:28
Abhishek009 wrote:
Luca1111111111111 wrote:
nick1816 wrote:
6x^2 -13x + 6 = 0
(3x-2)(2x-3)=0
Smaller root=2/3
Larger root=3/2
2/3*k=3/2
k=9/4

I find it difficult to transfrom 6x^2 -13x + 6 = 0 into (3x-2)(2x-3)=0
Is there a trick?


Yes there certainly is a formula for solving this , \(x\) = \(\frac{-b \pm \sqrt{b^2-4ac}}{2a}\) if \(b^2>4ac\)



Can you solve using this formula as an example ?
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 =   [#permalink] 02 Jun 2019, 13:28
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