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# In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?

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Intern
Joined: 03 Mar 2018
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In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis? [#permalink]

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06 Mar 2018, 11:40
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In x-y plane, does parabola y=$$ax^2$$+bx+c intersect to x-axis?

1) b= -2
2) c<0
[Reveal] Spoiler: OA
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 890
Location: India
Re: In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis? [#permalink]

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07 Mar 2018, 02:47
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itisSheldon wrote:
In x-y plane, does parabola y=$$ax^2$$+bx+c intersect to x-axis?

1) b= -2
2) c<0

In case of a parabola(quadratic expression) ax^2 + bx + c:
If parabola intersects x-axis at two distinct points, it means the quadratic expression has two distinct real roots, and this happens when (b^2 - 4ac) > 0
If parabola intersects x-axis at one point only, it means the quadratic expression has one real root, and this happens when (b^2 - 4ac) = 0
If parabola does not intersect x-axis at all, it means the quadratic expression has no real root, and this happens when (b^2 - 4ac) < 0

So we need to know the sign of (b^2 - 4ac).

Statement 1
b is negative, but we don't know anything about a and c. Not sufficient.

Statement 2
c is negative, but we don't know anything about a and b. Not sufficient.

Combining the two statements,
b and c are negative, but we don't know the sign of a.
If a is positive, then - 4ac will be positive, and then (b^2 - 4ac) will also be positive and the parabola will intersect x-axis.
If a is negative, then -4ac will be negative, and (b^2 - 4ac) could be either negative or positive or 0 depending on the magnitudes of a, b, c. So we cant say whether parabola will intersect x-axis or not.

So not sufficient to determine.

Re: In x-y plane, does parabola y=ax^2+bx+c intersect to x-axis?   [#permalink] 07 Mar 2018, 02:47
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