Quadratic Equation Quiz with Free PDF for SBI PO Pre 2021 , NRA CET , RRB Scale 1 Pre at Smartkeeda

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
Important for :
1
I. x2 – 4√3x + 9 = 0

II. y2 – √3y – 18 = 0
» Explain it
E
I. x2 – 4√3x + 9 = 0

x2 – 3√3x – √3x + 9 = 0

x(x – 3√3) – √3 (x – 3√3) = 0

(x – 3√3)(x – √3) = 0

x = √3, 3√3

II. y2 – √3y – 18 = 0

y2 + 2√3y – 3√3y – 18 = 0

y(y + 2√3) –  3√3 (y + 2√3) = 0

(y + 2√2)(y – 3√3) = 0

y = –2√3, 3√3

For x = 3√3, and y = 3√3     x = y

For x = 3√3, and y = –2√3  x > y

For x = √3, and y = –2√3  x > y

For x = √3,  and y = 3√3  x < y

Therefore, relationship can’t be established

Hence, option E is correct.
2
I. x2 – 9x + 20 = 0

II. 2y2 – 15y + 28 = 0
» Explain it
C
I. x2 – 9x + 20 = 0

x2 – 5x – 4x + 20 = 0

x(x – 5) – 4 (x – 5) = 0

(x – 5)(x – 4) = 0

x = 5, 4

II. 2y2 – 15y + 28 = 0

2y2 – 8y – 7y + 28 = 0

2y(y – 4) – 7(y – 4) = 0

(y – 4)(2y – 7) = 0

 y = 4, 7 2

 For x = 5, and y = 4, 7 x > y 2

For x = 4, and y = 4 x = y

For x = 4, and y = 3.5 x > y

Therefore, x ≥ y

Hence, option C is correct.

3
I. x2 – x – 20 = 0

II. y2 + y – 30 = 0
» Explain it
E
I. x2 – x – 20 = 0

x2 – 5x + 4x – 20 = 0

x(x – 5) + 4(x – 5) = 0

(x – 5)(x + 4) = 0

x = 5, –4

II. y2 + y – 30 = 0

y2 + 6y – 5y – 30 = 0

y(y + 6) – 5(y + 6) = 0

(y – 5)(y + 6) = 0

y = –6, 5

For x = 5, and y = 5, –6,   x ≥ y

For x = –4, and y = –6,   x > y

For x = –4, and y = 5, x < y

Therefore, relationship can’t be established

Hence, option E is correct.

4
I. x2 – 9x + 18 = 0

II. y2 – 9√2y + 36 = 0
» Explain it
E
I : x2 – 9x + 18 = 0

x2 – 6x –3x + 18 = 0

x(x – 6) –  3(x – 6) = 0

(x – 6)(x – 3) = 0

x = 3, 6

II :  y2 – 9√2y + 36 = 0

y2 – 3√2y  – 6√2y + 36 = 0

y(y – 3√2) –  6√2 (y  – 3√2) = 0

(y – 6√2)(y – 3√2) = 0

y = 6√2, 3√2

For x = 3  and y = 6√2 or 3√2   x < y

For x = 6 and y =  6√2              x < y

For x = 6 and y = 3√2               x > y

Therefore, relationship can’t be established

Hence, option E is correct.

5
I. x2 – 9 = 0

II. 2y2 + 13y + 21 = 0
» Explain it
C
I: x3 – 9 = 0

x = 3, –3

II: 2y2 + 13y + 21 = 0

2y2 + 7y + 6y + 21 = 0

y(2y + 7) + 3(2y + 7) = 0

(y + 3)(2y + 7) = 0

 y = –3, – 7 = –3.5 2

For x = –3 and y = –3, x = y

For x = –3 and y = –3.5 x > y

For x = 3, and y = –3 or –3.5 x > y

Therefore, x ≥ y

Hence, option C is correct.

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Folks, here is a another quiz of Quadratic Equation, so we are going to discuss different kind of Quadratic Equation questions which are frequently asked in IBPS PO Exams, So Quadratic Equation have a lot of chance to appear in IBPS PO 2018.

We have to solve both of the Quadratic equations to get to know the relation between both the variables.

Suppose we have two variables ‘x’ and ‘y’. The relationship between the variables can be any one of the following:

x > y
x < y
x = y or relation can’t be established between x & y
x ≥ y
x ≤ y

Meaning of different symbols, Before getting deep into the quadratic equations, lets try to understand the meaning of the basic operations used in finding the relationship between the variables –

(1) ‘>’ symbol: This symbol indicates that variable on the left side is definitely greater than the variable on the right side of the symbol.

For example:  x > y means x is definitely greater than y.
(2) ‘<’ symbol: This symbol indicates that variable on the left is definitely smaller than the variable on the right side of the symbol.
For example: x<y means x is definitely smaller than y.

(3) ‘=’ symbol: This symbol indicates that variable on the left side is equal to the variable on the right side of the symbol.
For example: x = y means x is definitely equal to y.

(4) ‘≥’ symbol: This symbol indicates that variable on the left side is either greater than or equal to the variable on the right side of the symbol.
For example:  x ≥ y means x is either greater than y or equal to y.
(5) ‘≤’ symbol: This symbol indicates that variable on the left side is either smaller than or equal to the variable on the right side of the symbol.

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

General form of a Quadratic Equation
ax2 + bx + c = 0

Quadratic equation means that it will definitely have the maximum power of the variable as ‘2’ which means we will always see ax2 term in a quadratic equation.

Or we can say that b can be 0, c can be 0 but a will never be 0.

While solving quadratic equation, you will always get 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.

Here are different kind of example of Quadratic Equation , so that we will get a very clear concept of the basic formation of a quadratic equation to get prepared for IBPS PO Pre 2018.

Type 1: This is basic of quadratic equation for bank exams like IBPS clerk Pre, SBI Clerk Pre, NIACL Assistant Pre as shown below

I. x3 – 4913 = 0                       II. y2 – 361 = 0

Here is the link to practice a proper quiz for quadratic equation for bank clerk pre exams like, IBPS Clerk pre 2018 SBI Clerk pre  and NIACL Assistant Pre

Type 2: Root based Quadratic Equation, these type of quadratic equation is being asked in IBPS PO Pre, SBI PO Pre exams

I. x2 – 3√3x – 54 = 0               II. y2 – 7√2y – 36 = 0

Here is the link to Practice New Pattern Based Quadratic Equation for IBPS PO 2018

Type 3: High level Quadratic Equation for IBPS PO 2018, this kind of Quadratic has been shown in many bank po exams

I. 20x2 – 108x + 144 = 0

II. 8y2 + 18y + 4 = 0