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

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

Hence, Answer is A

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