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# If one of the roots of the equation

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Director
Joined: 16 May 2014
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If one of the roots of the equation [#permalink]  27 Mar 2016, 23:13
Expert's post
00:00

Question Stats:

45% (01:26) correct 54% (02:20) wrong based on 11 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
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 97

Kudos [?]: 485 [2] , given: 64

Re: If one of the roots of the equation [#permalink]  28 Mar 2016, 00:30
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Expert's post

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]  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
Director
Joined: 20 Apr 2016
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Re: If one of the roots of the equation [#permalink]  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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