Question: Which of the following equations has a solution in common with x^2 - 2?
- x^2 - 6x + 9 = 0
- x^2 + 2x - 15 = 0
- 2x^2 + 9x + 9 = 0
- 2x^2 + x - 3 = 0
- none of the above
“Which of the following equations has a solution in common with x^2 - 2”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
We need to solve the original equation: x² - 2x - 15 = 0
We will do the 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, let us start by plugging x = -3 into the answer choices one by one:
Considering option A.
(-3)² - 6(-3) + 9 = 36.
Not good since we need it to evaluate to equal 0
Considering option B.
(-3)² + 2(-3) - 15 = -12.
Not good since we need it to evaluate to equal 0
Considering option C.
2(-3)² + 9(-3) + 9 = 0.
This is perfect.
x = -3 is a solution to this equation.
Correct Answer: C
Approach Solution 2:
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,
Correct Answer: C
Approach Solution 3:
We will see if any value satisfies any equation:
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
So we will check option C.
We can use -3 in the given options
C. 2x^2 + 9x + 9 = 0
18 - 27 + 9 =0
Correct Answer: C
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