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Which of the following equations has a solution in common with x^2 - 2

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Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 15 Aug 2016, 03:54
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:44) correct 46% (01:49) wrong based on 278 sessions

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Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 15 Aug 2016, 04:45
Bunuel wrote:
Which of the following equations has a solution in common with x^2 - 2x - 15 = 0?

A. x^2 - 6x + 9 = 0
B. x^2 + 2x - 15 = 0
C. 2x^2 + 9x + 9 = 0
D. 2x^2 + x - 3 = 0
E. none of the above



Given : x^2 - 2x - 15 => (x+3) (x-5) = 0 => 5 and -3 are the roots..

A. x^2 - 6x + 9 = 0 => (x-3) (x-3)
B. x^2 + 2x - 15 = 0 => (x+5) ( x-3)
C. 2x^2 + 9x + 9 = 0 => (x+3) ( 2x+3)
D. 2x^2 + x - 3 = 0 => (x-1) (2x+3).... no eq has same roots as per the parent eq..

IMO C is correct answer..has it has x+3

OA please...will correct if I missed anything..
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Re: Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 15 Aug 2016, 07:34
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Bunuel wrote:
Which of the following equations has a solution in common with x² - 2x - 15 = 0?

A. x² - 6x + 9 = 0
B. x² + 2x - 15 = 0
C. 2x² + 9x + 9 = 0
D. 2x² + x - 3 = 0
E. none of the above


msk0657's solution is great. Here's another approach to consider if your factoring skills are not strong, and it takes you a while to factor.

Solve the original equation: x² - 2x - 15 = 0
Factor to get: (x + 3)(x - 5) = 0
This means EITHER x + 3 = 0, in which case x = -3...
OR x - 5 = 0, in which case x = 5

At this point, we're looking for an answer choice that has EITHER x = -3 OR x = 5 as a solution.
So, start by plugging x = -3 into the answer choices:
A. (-3)² - 6(-3) + 9 = 36. No good. We need it to evaluate to equal 0
B. (-3)² + 2(-3) - 15 = -12. No good. We need it to evaluate to equal 0
C. 2(-3)² + 9(-3) + 9 = 0. PERFECT! x = -3 IS a solution to this equation

Answer:

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Re: Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 16 Jul 2017, 12:19
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Which of the following equations has a solution in common with \(x^2 - 2x - 15 = 0\)?

\(x^2 - 2x - 15 = 0\)

\(x^2 - 5x + 3x - 15 = 0\)

\((x - 5) (x + 3) = 0\)

\(x = 5\) OR

\(x = -3\)

We can directly check by plugging these values into the equations given in the answer choices.

Or you can solve the below equations to see if the value is matching as per above equation.

A. \(x^2 - 6x + 9 = 0\) ==> \((x-3)(x-3) = x = 3\) =====> NOT Matching - Hence, Out

B. \(x^2 + 2x - 15 = 0\) ==> \((x+5)(x-3) = x = -5 or x = 3\) =====> NOT Matching - Hence, Out

C. \(2x^2 + 9x + 9 = 0\) ==> \((2x+3)(x+3) = x = -3/2 Or x = -3\) =====> As the value -3 is matching to the solution of the above equation. this is as the corect asnwer.

D. \(2x^2 + x - 3 = 0\) ==> (\(x-1) (2x+3) = x = 1 Or x = -3/2\) =====> NOT Matching - Hence, Out

E. none of the above

Hence, Answer is A

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Re: Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 20 Jul 2017, 16:38
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Bunuel wrote:
Which of the following equations has a solution in common with x^2 - 2x - 15 = 0?

A. x^2 - 6x + 9 = 0
B. x^2 + 2x - 15 = 0
C. 2x^2 + 9x + 9 = 0
D. 2x^2 + x - 3 = 0
E. none of the above


Factoring the given equation, we have:

x^2 - 2x - 15 = 0

(x - 5)(x + 3) = 0

x = 5 or x = -3

Let’s factor down each answer choice:

A. x^2 - 6x + 9 = 0

(x - 3)(x - 3) = 0

x = 3

Answer choice A is not correct.

B. x^2 + 2x - 15 = 0

(x + 5)(x - 3) = 0

x = -5 or x = 3

Answer choice B is not correct.

C. 2x^2 + 9x + 9 = 0

(2x + 3)(x + 3) = 0

x = -3/2 or x = -3

We see that this equation has a solution in common with x^2 - 2x - 15 = 0, and thus answer choice C is correct.

Answer: C
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Re: Which of the following equations has a solution in common with x^2 - 2  [#permalink]

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New post 26 Jan 2019, 04:18
Bunuel wrote:
Which of the following equations has a solution in common with x^2 - 2x - 15 = 0?

A. x^2 - 6x + 9 = 0
B. x^2 + 2x - 15 = 0
C. 2x^2 + 9x + 9 = 0
D. 2x^2 + x - 3 = 0
E. none of the above


x^2 - 2x - 15 = 0, just factor this equation to get roots as -3 or 5

Now out of the options one has a common root in -3 or 5

We can use -3 in the given options

Only C satisfies the equation

C. 2x^2 + 9x + 9 = 0

18 - 27 + 9 =0
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Re: Which of the following equations has a solution in common with x^2 - 2   [#permalink] 26 Jan 2019, 04:18
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