QUADRATIC EQUATION COMPARISON SHORTCUT

Dear friends,

QUADRATIC COMPARISON is the most common topic in compteative exams. Quadratic comparison come in the set of 5-6 question in the Quant section. Time required to solve the question probably is around 15-30 sec which can be the game changer in time bound exam like MH-CET .

Mostly,

Two quadratic equation are given.

We have to compare the two Quadratic equation and find out realtion between two of them.

Lets suppose

We have two quadratic equation

1} ax2 + bx + c = 0

2} ay2 + by + c = 0

a, b and c are known values

a can't be 0.

"x&y" are the variable or unknown (we don't know it yet).

☆The relationship between the variables "X&Y" can be any one of the following:☆

▪x>y : means x is definitely greater than y.

▪x<y : means x is definitely smaller than y.

▪x=y : means x is definitely equal to y.

▪relation can’t be established between x & y

▪x≥y: means x is either greater than y or equal to y.

▪x≤y:means x is either smaller than y or equal to y.

For example

In the following questions, there are two equations (I) and (II). Solve the equations and answer accordingly:

1) x2 +7x +10 = 0

2) 2y2-7y + 6 = 0

Solution:

Solving equation I:

x2 +7x+10 = 0

x2 +5x+2x+10 = 0

x(x+5)+2(x+5) = 0

(x+2)(x+5) = 0

x =-5 and -2. {Roots of equation 1}

Solving equation II:

2y2 -7y + 6 = 0

2y2 -4y-3y + 6 = 0

2y(y-2)-3(y-2)=0

(y-2)(2y-3)=0

Y=3/2 and 2. {Roots of equation 2}

y=1.5 and 2

NOW comparing both roots on number line thus quadratic equation comparison x and y .

Conclusion: Y is greater than X

Question asked in Exam SAMPLE

1. In the question below, 2 equations are given. Solve both the equation and choose the correct option.

I. x2 – 4x + 3 = 0

II. y2 – 13y + 40 = 0

Options

a. x > y

b. x ≥ y

c. x < y

d. x ≤ y

e. x = y or Cannot be determined.

☆METHODS FOR ROOT FINDING☆

There are various MATHEMATICAL and GRAPHICAL methods for root finding but we need to solve problem in 15 sec hence some alternative had to consider.

Whenever we solve a quadratic equation, we will get exactly 2 values of the equation. These 2 values are called roots of the equation. The roots of the equation always satisfy the equation. So in case of doubt, we can check the solution by putting the values back into the equation. If the equation turns out to be zero then our roots are correct

Following link shows the best shortcut to solve the quadratic equation comparison x and y