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07 Jun 2018, 02:41
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
72% (00:49) correct
28%
(01:14)
wrong
based on 169
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[GMAT math practice question]
In the x-y plane, does the parabola \(y=ax^2+bx+c\) have x-intercepts?
\(1) b^2-4ac<0\)
\(2) a<0\)
In the x-y plane, does the parabola \(y=ax^2+bx+c\) have x-intercepts?
\(1) b^2-4ac<0\)
\(2) a<0\)
07 Jun 2018, 03:10
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MathRevolution
The value \(b^2-4ac\) is called discriminant and it has the following properties:
1) If \(b^2-4ac>0\), then the equation \(ax^2+bx+c=0\) has two roots or in other words, the parabola has two \(x\)-intercepts.
2) If \(b^2-4ac<0\), then the equation \(ax^2+bx+c=0\) has no roots or in other words, the parabola does not have \(x\)-intercept.
3) If \(b^2-4ac=0\), then the equation \(ax^2+bx+c=0\) has one single root or in other words, the parabola has one single \(x\)-intercept.
(1) The parabola does not have \(x\)-intercepts. Answer is NO. Sufficient.
(2) We don't know whether the discriminant is positive, negative or zero. Not sufficient.
Answer: A
General Discussion
07 Jun 2018, 03:15
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Statement 2 only tells us whether the parabola opens upwards or downwards.
Statement 1 on the other hand tells us that the roots of the equation are imaginary. This means that the parabola won't cut the x-axis.
Hence one can say that statement 1 is sufficient while 2 alone is not.
Statement 1 on the other hand tells us that the roots of the equation are imaginary. This means that the parabola won't cut the x-axis.
Hence one can say that statement 1 is sufficient while 2 alone is not.
