33. The graph of which of the following equations have two intersections with axis-x?
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(C) y=-3x^2-5x+7
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1
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Rahul@gurome
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On x-axis, y = 0
If (b^2 - 4ac) > 0 for the equation ax^2 + bx + c = 0, then it gives 2 real roots, and intersects the x-axis in 2 points.
(A) x^2+2x+3 = 0 implies b^2 - 4ac = 4 -12 < 0, implies 2 conjugate imaginary roots, which implies it does not intersect x -axis.
(B) 2x^2-3x+6 = 0 implies b^2 - 4ac = 9 - 48 < 0, implies 2 conjugate imaginary roots, which implies it does not intersect x -axis.
(C) -3x^2-5x+7 = 0 implies b^2 - 4ac = 25 + 84 > 0, which implies equation has 2 real roots, implies it intersects the x -axis in 2 points.
[spoiler]The correct answer is (C).[/spoiler]
If (b^2 - 4ac) > 0 for the equation ax^2 + bx + c = 0, then it gives 2 real roots, and intersects the x-axis in 2 points.
(A) x^2+2x+3 = 0 implies b^2 - 4ac = 4 -12 < 0, implies 2 conjugate imaginary roots, which implies it does not intersect x -axis.
(B) 2x^2-3x+6 = 0 implies b^2 - 4ac = 9 - 48 < 0, implies 2 conjugate imaginary roots, which implies it does not intersect x -axis.
(C) -3x^2-5x+7 = 0 implies b^2 - 4ac = 25 + 84 > 0, which implies equation has 2 real roots, implies it intersects the x -axis in 2 points.
[spoiler]The correct answer is (C).[/spoiler]
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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guessing method
as we know that , if an equation contains x^2 ,then the graph must be parabola. and parabola intersects with axis 2 times ,depending on the sign ( it can be also that , parabola will situate above the axis). as all equation are parabola , then we must seek something ,that is differing only one equation from others (especially sign,because mostly it depends on this the draw of parabola).
all this equations are the same ,almost. and you can't simplify them.
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1
only C ( y=-3x^2-5x+7) has a different sign of x.
by this method it's easy find an answer, within seconds.
as we know that , if an equation contains x^2 ,then the graph must be parabola. and parabola intersects with axis 2 times ,depending on the sign ( it can be also that , parabola will situate above the axis). as all equation are parabola , then we must seek something ,that is differing only one equation from others (especially sign,because mostly it depends on this the draw of parabola).
all this equations are the same ,almost. and you can't simplify them.
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1
only C ( y=-3x^2-5x+7) has a different sign of x.
by this method it's easy find an answer, within seconds.
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GMATGuruNY
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The graphing of quadratic equations (parabolas) is not tested on the GMAT, so you shouldn't worry about this type of problem.mehulv wrote:33. The graph of which of the following equations have two intersections with axis-x?
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(C) y=-3x^2-5x+7
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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