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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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15 Aug 2016, 02:54
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65% (hard)

Question Stats:

55% (01:45) correct 45% (01:49) wrong based on 242 sessions

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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

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

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15 Aug 2016, 03:45
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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15 Aug 2016, 06:34
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Top Contributor
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

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

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16 Jul 2017, 11:19
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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

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

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20 Jul 2017, 15:38
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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.

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

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26 Jan 2019, 03:18
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, 03:18
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