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by shivanigs » Tue Oct 02, 2012 11:18 pm
Hi,

Request help with the following question.Thanks..

Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

1. a < 0
2. c > 0
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Oct 03, 2012 12:45 am
For the function f(x) = y = to intersect with the x - axis, y should be 0.
=> ax^2 + c = 0
x^2 = -c/a
so we will have real roots if x^2 is positive or zero.

1) a < 0
x^2 = -c/a, x^2 is positive when c is +ve
if c is -ve, we will have imaginary roots.
so can`t answer with option 1 alone.

2) c > 0
x^2 = -c/a, x^2 is positive when a is -ve.
if a is +ve, we will have imaginary roots.
so can`t answer with option 2 alone.

taking option 1 and 2.
we have x^2 = +ve, hence it has real roots. so it will intersect x-axis.

Hence, it is C
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