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By what factor should the smaller root of the equation 6x^2-3x+6 =

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Senior Manager
Joined: 18 Feb 2019
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GMAT 1: 460 Q42 V13
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By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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29 Mar 2019, 00:27
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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
Director
Joined: 18 Jul 2018
Posts: 895
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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29 Mar 2019, 11:24
$$6x^2-13x+6 = 0$$
roots of the equation = $$(-b±\sqrt{b^2-4ac})/2a$$
b = -13
a = c = 6
$$(13±\sqrt{169-144})/12$$ = $$\frac{13 ± 5}{12}$$ = 3/2 or 2/3.
Smaller root = 2/3.
It should be increased by a factor to make it equal to the larger factor = (3/2)/(2/3) = 9/4

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Joined: 22 Mar 2019
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Re: By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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31 Mar 2019, 20:39
How do we deduce that this "increase" must be a multiplication factor and not an additional factor ?
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Joined: 12 Sep 2017
Posts: 245
Re: By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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13 Apr 2019, 18:09
Just factorize

$$6x^2 - 13x + 6 = 0$$

$$(x-9)(x-4) = 0$$

Roots: 9 and 4.

Smaller one 4.

$$9 = 4x$$

$$x$$ = $$\frac{9}{4}$$

E
Re: By what factor should the smaller root of the equation 6x^2-3x+6 =   [#permalink] 13 Apr 2019, 18:09
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