How many roots does x6 –12x4 + 32x2 = 0 have?(A) 1(B) 3(C) 4(D) 5(E) 2Solution:x^6 –12(x^4) + 32(x^2) = x^2 (x^4 – 12x^2 + 32) = x^2 (x^2 – 4)(x^2 – 8)The roots are 0, ±2, and ±2√2: a total of 5.Please remember that ‘0’ is also a root.The correct answer is D … [Read more...] about Equations – roots and powers

# GMAT Algebra Theory & Practice Questions

## GMAT Inequalities, Quadratic Equation

Inequalities is a big favorite of the GMAT test makers. Inequalities, especially presented as a data sufficiency question that appear in the GMAT test are many a times potential land mines.Here is an inequality question in the problem solving formatWhich of the following is correct if x is a real number and (x - 11)(x - 3) is negative?A. x^2 + 5x + 6 < 0B. x^2 + 5x + 6 > 0C. 5 … [Read more...] about GMAT Inequalities, Quadratic Equation

## GMAT PS : Quadratic Equation : Parabola cutting x-axis

Here is a question testing concepts of Quadratic equation and nature of roots of quadratic equation. If y = x2 + dx + 9 does not cut the x-axis, then which of the following could be a possible value of d? I. 0 II. -3 III. 9 A. III only B. II only C. I and II only D. II and III only E. I and III only Correct Answer : Choice C. Values that 'd' could take are 0 or … [Read more...] about GMAT PS : Quadratic Equation : Parabola cutting x-axis

## Quadratic Equations : Sum & Product of roots

Quadratic equations are equations of the form ax2 + bx + c = 0. A quadratic equation has two roots. These roots are found either by factorizing the quadratic equation or by using the formula $latex \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}&s=3$ Here is a typical quadratic equation question If m and n are the roots of the quadratic equation x2 - (2 √ 5)x - 2 = 0, the value of m2 + … [Read more...] about Quadratic Equations : Sum & Product of roots

## Data Sufficiency : Number Properties & Equations

About a third of the questions that appear on the Quantitative section of the GMAT CAT test are data sufficiency (DS) questions. Here is a DS question from Number properties and number theory. Number properties and number theory is a hot favorite when it comes to setting DS questions.For the uninitiated amongst us, this is how the instructions to a DS question will look … [Read more...] about Data Sufficiency : Number Properties & Equations