GMAT Quant: Algebra – Quadratic Equations

GMAT Quadratic Equations

Any form of the equation having second-degree polynomial in one variable is called quadratic equation. Typically in GMAT you have to deal with the  equation form of y = ax2 + bx + c formula related to the quadratic equations that you need to mug up is

  1. Root of the the equation ax2 + bx + c = 0 is

8

  1. Determinant D is calculated as

9

If D=0, equation will have real and equal root

If D>0, equation will have real roots

If D<0, equation will have imaginary roots

Let’s look at some problems

  1. The sum of a number and its reciprocal is 10/3. Find the number.

Let the number be x.therefore x +1/x=10/3

Arranging the equation we get,

3x210x + 3 = 0

(3x-1)(x-3) = 0

Therefore, x = 3, ⅓

  1. If x2 + bx + 72 = 0 has integral roots, find the number of values b can attain.

72 can be written as 2 x 2 x 2 x 3 x 3. Hence the number of positive pairs whose product is 72 is (3+1)(2+1)/2= 6.

Similarly, the number of negative pairs are 6. Hence 12 is the answer.

Also Read:
GMAT Data Sufficiency
GMAT Problem Solving
GMAT Quant Study Plan

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