MathRevolution wrote:
[GMAT math practice question]
In the x-y plane, does the parabola \(y=ax^2+bx+c\) have x-intercepts?
\(1) b^2-4ac<0\)
\(2) a<0\)
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 _________________