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

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

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New post 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
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By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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New post 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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Re: By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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New post 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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Re: By what factor should the smaller root of the equation 6x^2-3x+6 =  [#permalink]

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

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