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

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Bunuel
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By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink] New post   21 Oct 2021, 01:30
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52% (01:53) correct 48% (01:57) wrong based on 52 sessions
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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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100mitra
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink] New post   21 Oct 2021, 05:18
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= 6X^2 - 13X + 6
= 6X^2 - 9X - 4X + 6
= (6X - 9)(6X - 4)
= X { 3/2 , 2/3}

Smaller root = 2/3
Smaller root multiplied by (2/3) * (9/4) = (3/2) larger root

Correct Option E

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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink] New post   21 Oct 2021, 05:32
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6x^2−13x+6=0
6x^2 - 9x - 4x + 6 =0
= 3x (2x -3) - 2(2x-3)=0
=(3x-2) (2x-3)
=3x = 2
x=2/3

2x=3
x=3/2

Smaller root = 2/3
Large root = 3/2
Factor the smaller root needs to be increased to be equal to larger root = 3/2 *3/2 =9/4

IMO E
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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink] New post   21 Oct 2021, 05:58
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Converting equation to standard Quadratic, sum of roots = 13/6, product of roots = 1.

Since determinant is >0, plugging simple reciprocal numbers gives 2/3 & 3/2 adding upto 13/6

Answer will essentially be (larger root)^2.

Hence, 3/2*3/2= 9/4

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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink] New post   03 Nov 2021, 07:50
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Bunuel 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


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Re: By what factor should the smaller root of the equation 6x^2 -13x + 6 = [#permalink]
03 Nov 2021, 07:50
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