Quadratic Equation for IBPS PO 2021 , NRA CET , SBI Clerk Mains , IBPS RRB PO , IBPS RRB Clerk and RBI Assistant Mains Exams with Detailed Solution

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
» Explain it
B
I. 20x2 + 29x – 36 = 0

20x2 + (45 – 16)x – 36 = 0

20x2 + 45x – 16x – 36 = 0

5x (4x + 9) 
– 4 (4x + 9) = 0

(4x + 9) (5x – 4) = 0

x = – 9/4, 4/5

II.  5y2 – 14y + 8 = 0

5y2 – (10 + 4)y + 8 = 0

5y2 – 10y – 4y + 8 = 0

5y (y 
– 2) – 4 (y – 2) = 0

(y 
– 2) (5y – 4) = 0

y = 2, 4/5 

While comparing the root values of x and y, we find that both the values of x are less than y's. Therefore, x 
≤ y

Hence, option B is correct.
2
» Explain it
E
I. (x + 6) ( 8 –  1 )  = 0
x

(x + 6) (   8x – 1 )  = 0
x

(x + 6) (8x – 1) = 0

x = – 6, 1/8

II. y2 + √576 = √1089

y2 + 24 = 33

y2 = 9

y = 3,  –3

Relationship between x and y cannot be established.

Hence, option E is correct.
» Explain it
B
I. x4 × 612 = x6 × 17 

612 = x2 × 17

x2 = 36

x  = ± 6

II. y2/3 × 102 = 17 × y5/3

y5/3 ÷ y2/3 = 6

y(5/3 – 2/3) = 6

y = 6

x ≤ y

Hence, option B is correct.
» Explain it
E
I. 88x2 – 7x – 15 = 0

88x2 – (40 – 33)x – 15 = 0

88x2 – 40x + 33x – 15 = 0

8x (11x – 5) + 3 (11x – 5) = 0

(8x + 3) (11x – 5) = 0

x = 5/11, – 3/8

II. 27y2 – 6y – 8 = 0

27y2 – (18 – 12)y – 8 = 0

27y2 – 18y + 12y – 8 = 0

9y (3y – 2) + 4 (3y – 2) = 0

(3y – 2) (9y + 4) = 0

y = 2/3, – 4/9

While comparing the root values of x and y, both the values of x's lies between the values of y's.

Hence, option E is correct.
5
I. x3 + 4913 = √6561                     

II. (√y – 4)  ( √y  – 1 )  = 0
2
» Explain it
B
I. x3 + 4913 = 6561

x3 + 17 = 81

x3 = 81 – 17

x3 = 64

x = 4

II. (√y – 4)  ( √y  – 1 )  = 0
2

(√y – 4) 
(√y – 2)
 = 0
2

(√y – 4) (√y – 2) = 0

√y – 4 = 0, √y – 2 = 0

y = 16, 4

x ≤ y

Hence, option B is correct.

Difficult Quadratic Equation Questions Examples at Smartkeeda


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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 SBI PO Pre Exam, So Quadratic Equation have a lot of chance to appear in SBI PO Pre 2020.
 
First of all we discuss different kind of Quadratic Equation for SBI PO Pre 2020 like New pattern based Quadratic Equation Question and Answer that are now being asked in the exams are high level and it can be based on root based quadratic equation and general Quadratic Equation, find out the root values and then compare them and last but not the least Shri Dharcharya Rule based Quadratic Equation, Quadratic Equation is one of the most favorite topics of SBI PO Pre 2020. Questions on Quadratic Equations are asked in Quantitative Aptitude section. Generally, two quadratic equations in two different variables are given.
 
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 SBI PO Pre 2020.
 
Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.
 
Quadratic Equation Question Type 1:
 
I. x2 – 9x + 18 = 0
II. y2 – 11y + 18 = 0
A. if x > y
B. if x ≤ y
C. if x ≥ y
D. if x < y
E. if x = y or relationship between x and y can't be established
 
Quadratic Equation Question Type 2:
 
I. x = 152 – 63
II. y = 122 – 112 – 14
A. if x > y
B. if x ≤ y
C. if x ≥ y
D. if x < y
E. if x = y or relationship between x and y can't be established
 
Quadratic Equation Question Type 3:
 
I. x2 – 14x + 48 = 0
II. y2  – 9y + 20 = 0
A. if x > y
B. if x ≤ y
C. if x ≥ y
D. if x < y
E. if x = y or relationship between x and y can't be established
 
Quadratic Equation Question Type 4:
 
I. 6x + y = 25
II. 2x + 3y = 27
A. if x > y
B. if x ≤ y
C. if x ≥ y
D. if x < y
E. if x = y or relationship between x and y can't be established
 
Quadratic Equation Question Type 5:
 
I. 4x + 3y = 51
II. x + 4y = 29
A. if x > y
B. if x ≤ y
C. if x ≥ y
D. if x < y
E. if x = y or relationship between x and y can't be established

I hope these Quadratic equations will help you in upcoming SBI PO Pre 2020 exams, if you want to practice a Mock Test for SBI PO Pre Based on IBPS PO Pre 2020  link is below:

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