banksy wrote:

SC) If equation ах^2 + bх + с = 0 have two distinct roots, which of the following must be true?

I. b > 0

II. ac > 0

III. ac < 0

(A) None

(B) I only

(C) II only

(D) III only

(E) I and II only

\(ax^2 + bx + c = 0\) will have 2 distinct roots (assumed to be real since we are dealing with GMAT here) when \(b^2 - 4ac > 0\)

(Note that when \(b^2 - 4ac = 0\), the roots are equal and when \(b^2 - 4ac < 0\), the roots are imaginary)

So \(b^2 > 4ac\) is the condition required.

Is it necessary that b should be positive? No. Even if b is negative, \(b^2\), which will be positive, can be greater than 4ac.

There is no condition at all on ac. It can be positive or negative. Just that \(b^2\) should be greater than it.

Hence we don't need any one of them to be necessarily true.

_________________

Karishma

Veritas Prep GMAT Instructor

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