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If one of the roots of the equation

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Director
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If one of the roots of the equation [#permalink] New post 27 Mar 2016, 23:13
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Question Stats:

49% (01:30) correct 49% (02:06) wrong based on 14 sessions
If one of the roots of the equation \(2x^2\) + (3k + 4)x + (\(9k^2\)–3k– 1) = 0 is twice the other, then which of the following can be a value of ‘k’?

A. \(\frac{-2}{3}\)

B. \(\frac{2}{3}\)

C. \(\frac{-1}{3}\)

D. \(\frac{1}{3}\)

E. None of the above
[Reveal] Spoiler: OA

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Director
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Re: If one of the roots of the equation [#permalink] New post 28 Mar 2016, 00:30
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Explanation


Let one of the roots of the given equation be ‘a’. Then, the other root will be ‘2a’.
∴ Sum of the roots = a + 2a = -(3k+4)/2
or, a = -(3k+4)/6 ----- (i)


∴ Product of the roots = a*2a = \(2a^2\)= \((9k^2-3k-1)/2\)
or, \(a^2\) = \((9k^2-3k-1)/4\) ---- (ii)

Combining (i) and (ii),
⇒ \(72k^2\)−51k−25 = 0
⇒(3k + 1)(24k − 25) = 0
Therefore, k = -1/3, 25/24.
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Re: If one of the roots of the equation [#permalink] New post 04 Jun 2019, 01:02
I did the backward calculation by taking the possible values of K. I tried to find whether the reformed equation ( in line with the value of K) gives two roots or not and the roots corroborate to the conditions or not. Eventually , whiling taking K=-1/3, It matched the conditions. Thus, I got C.
But this was too time-consuming.
Can any of you please give an easy and quicker solution ?
Regards
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Re: If one of the roots of the equation [#permalink] New post 12 Jun 2019, 05:30
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JelalHossain wrote:
I did the backward calculation by taking the possible values of K. I tried to find whether the reformed equation ( in line with the value of K) gives two roots or not and the roots corroborate to the conditions or not. Eventually , whiling taking K=-1/3, It matched the conditions. Thus, I got C.
But this was too time-consuming.
Can any of you please give an easy and quicker solution ?
Regards



The solution provided above is less time consuming.

Whenever u receive a complex quadratic equation "\(ax^2 + bx + C\) " and need to find the roots, the best way is to know

1. Sum of the roots = \(-\frac{b}{a}\)

2. product of the roots = \(\frac{c}{a}\)
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Re: If one of the roots of the equation   [#permalink] 12 Jun 2019, 05:30
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