quadratic equations Model Questions & Answers, Practice Test for ibps clerk prelims 2023
ibps clerk prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Trigonometric Ratios & Identity
Linear Equations
Quadratic Equations
Logarithm
If α and β are the roots of the equation $ax^2$ + bx + c = 0, then what is the value of the expression (α + 1) (β + 1) ?
Answer: (a)
Directions :
In each of these questions, two equations numbered I and II are given. You have to solve both the equations and –
- if x < y
- if x ≤. y
- if x > y
- if x ≥ y
- if x = y or the relationship cannot be established.
I. $x^2$ – 22x + 120 = 0
II. $y^2$ – 26y + 168 = 0
Answer: (b)
Note: Let the quardatic equation be $ax^2$ + b + c = 0.
To find roots of this equation quickly, we find two factors of 'b' such that their sum is equal to b and their product is equal to the product of the coefficient of x2 and the constant term 'c'.
Let two such factors be α and β.
The α + β = b and α β = ca
In the second step, we divide these factors by the coefficient of $x^2$ ,
ie be 'a'.
In the next step, we change the signs of the outcome. These are the
roots of the equation.
Directions :
In the following questions, two equations numbered I and II are given. You have to solve both the equations and –
- if x > y
- if x ≥. y
- if x < y
- if x ≤ y
- if x = y or the relationship cannot be established.
I. x – $√{121}$ = 0
II. $y^2$ – 121 = 0
Answer: (b)
x = $√{121}$ = 11, $y^2$ = 121, y = ± 11
If $x^2$ + 7x + 12 = 0 and $y^2$ + 9y + 20 = 0, then what is the relation between x and y?
Answer: (a)
![quadratic-equations-mcq-problems-competitive-exams-quantitative-aptitude quadratic-equations-mcq-problems-competitive-exams-quantitative-aptitude](https://careericons.com/adminicon/bunch/images/quadratic-equations-mcq-problems-competitive-exams-3-1.png)
x = – 3, – 4
y = – 4, – 5
∴ x ≥ y
2-6 :
If $3^x + 27(3^{-x})$ = 12, then what is the value of x ?
Answer: (a)
Given, $3^x + 27(3^{-x})$ = 12
Let $3^x$ = y
∴ y + ${27}/y$ = 12
⇒ $y^2$ - 12y + 27 = 0
⇒ $y^2$ - 9y - 3y + 27 = 0
⇒ (y - 3) (y - 9) = 0 ⇒ y = 3, 9
when y = 3; when y = 9;
⇒ $3^x = 3; 3^x = 9$
∴ x = 1 x = 2
x = 1, 2 are value of x.
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