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# In how many places does the graph of the equation y = ax^2 + bx + c in

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VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1343
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
In how many places does the graph of the equation y = ax^2 + bx + c in  [#permalink]

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05 Jul 2018, 09:40
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:23) correct 33% (01:18) wrong based on 20 sessions

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In how many places does the graph of the equation y = ax^2 + bx + c intersect the x - axis?

1. $$ac = 4$$

2.$$\sqrt{b} = \sqrt{5}$$

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Director
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Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: In how many places does the graph of the equation y = ax^2 + bx + c in  [#permalink]

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05 Jul 2018, 11:22
QZ wrote:
In how many places does the graph of the equation y = ax^2 + bx + c intersect the x - axis?

1. $$ac = 4$$

2.$$\sqrt{b} = \sqrt{5}$$

Given equation y = ax^2 + bx + c is parabolic in nature.
Concept:-
1-If discriminant is positive parabola has two intercepts with x‐axis.
2-If discriminant is negative parabola has no intercepts with x‐axis.
3-If discriminant is zero parabola has one intercept with x‐axis.

Discriminant, $$D=b^2-4ac$$
clearly, St1 & st2 are not sufficient individually.

Combining, we have,ac=4 from st1, b=5 from st2
So, $$D=b^2-4ac$$=$$5^2-4*4=25-16=9>0$$

Since discriminant is negative, parabola has two intercepts with x‐axis.

Ans. (C)
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Re: In how many places does the graph of the equation y = ax^2 + bx + c in &nbs [#permalink] 05 Jul 2018, 11:22
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