Maths Tips

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D is called the Discriminant of a quadratic equation.

D = b2 - 4ac for quadratic equations of the form ax2 + bx + c = 0.

If D > 0, roots of such quadratic equations are Real and Distinct

If D = 0, roots of such quadratic equations are Real and Equal

If D < 0, the roots of such quadratic equations are Imaginary. i.e., such quadratic equations will NOT have real roots.

In this GMAT sample question in algebra, we have to determine the largest integer value that ‘k’ can take such that the discriminant of the quadratic equation is positive.

For quadratic equations of the form ax2 + bx + c = 0, the sum of the roots = −b/a

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Inequality

(x-a)(x-b)>0

1. (x-a)(x-b) will be <0 when x is between a and b

2. (x-a)(x-b) will be >0 when x is other wise ( outside the roots)