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Quadratic Equations : Overview and Practice



Hi guys!

Today we are going to cover a seemingly scary looking but a quite simple section of GRE Quant - ALGEBRA!

There are going to be a lot of questions that you will encounter in your GRE that have an application of algebraic concepts. But do understand that the questions might look tough, but the underlying concept is just simple algebra.

This post covers a part of algebra - Quadratic Equations. We have started with an overview of the topic followed by practice questions.

In the subsequent sections, we will be posting more in relation to the concept. So, sit tight and keep practicing!

Overview

A quadratic equation is an equation of the form 

where x is unknown, and a, b and c are known constants. If a=0, then the equation is linear and not quadratic.
The quadratic equation has two roots given by
The nature of the roots is given by discriminant, D.
If
(1) D > 0 : The equation has two real roots and both roots are real and distinct.
(2) D = 0 : The equations has only two real roots but both roots are real and equal.
(3) D < 0 : The equation has two imaginary roots.

Practice Questions

(1) If S2 > T2 , which of the following must be true?

🔘S > T

🔘S2 > T

🔘|S| > |T|

🔘ST < 0

🔘ST > 0

Answer: |S| > |T|

(2) If (x+3)2 = 225, which of the following could be the value of x-1?

🔘13

🔘12

🔘-12

🔘-16

🔘-19

Answer:  -19

(3) If 3t3 -7=74, what is t2-t?

🔘3

🔘6

🔘-3

🔘18

🔘9

Answer: 6

(4) If x≠-y ,(x2+2xy+y2)/2(x+y)2

🔘1

🔘1/(x+y)

🔘1/2

🔘xy

🔘2xy

Answer:  ½

(5) If x+y=-3 and x2+y2=12,  what is the value of 2xy? (Numeric Entry)

 Answer: -3

(6) (x-2)2+(x-1)2+x2+(x+1)2+(x+2)2   

🔘5x2

🔘5x2+10

🔘x2+10

🔘5x2+6x+10

🔘5x2-6xy+10

Answer:  5x2+10

(7) If a=(x+y)2 and b=x2+y2   and xy>0, which f the following must be true? Indicate all such statements.

🔘a=b

🔘a>b

🔘a is positive

Answer: a>b, a is positive

(8) The maximum height reached by a ball thrown straight up into the air can be determined by the formula h = -16 vt + d, where t is the number of seconds since it was thrown, v is the initial speed of the throw (in feet per second), d is the height (in feet) at which the ball was released, and h is the height of ball 1 seconds after the throw. Two seconds after a ball is thrown, how high in the air is the ball if it was released at a height of 6 feet and a speed of 80 feet per second?

🔘96 feet

🔘100 feet

🔘102 feet

🔘134 feet

🔘230 feet

Answer : 102 feet


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