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

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