Max@Math Revolution wrote:[GMAT math practice question]
If f(x)=ax^2+bx+c, where a, b and c are integers, is b=0?
1) f(49)=f(-49)=0
2) f(0)f(49)=0
Statement 1:
Since (49, 0) and (-49, 0) are both solutions, the quadratic must be as follows:
f(x) = (x-49)(x+49) = x² - 49²
In the resulting quadratic, b=0.
Thus, the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
If x-49 is a factor of the equation, then f(49) = 0.
Case 1: f(x) = (x-49)(x+49) = x² - 49², with the result that f(0)f(49) = f(0) * 0 = 0
In this case, b=0, so the answer to question stem is YES.
Case 2: f(x) = (x-49)(x+1) = x² - 48x - 49, with the result that f(0)f(49) = f(0) * 0 = 0
In this case, b=-48, so the answer to the question stem is NO.
INSUFFICIENT.
The correct answer is
A.
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