Quadratic Equations Pdf Model Questions & Answers, Practice Test for ibps po prelims 2024 2025
ibps po prelims 2024 2025 SYLLABUS WISE SUBJECTS MCQs
Lcm & Hcf
Simplification
Power, Indices And Surds
Ratio & Proportion
Time & Work
Time & Distance
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Profit & Loss
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Compound Interest
Number Series
Quadratic Equations
Probability
Permutations & Combination
If one root of the equation $ax^2$ + bx + c = 0 is three times the other, then ______
Answer: (a)
Let α, 3α are the roots.
α + 3α = ${-b}/a$
⇒ 4α = ${-b}/a$
⇒ α = ${- b}/{4a}$ ...(1)
α × 3α - $c/a ⇒ 3a^2 - c/a$
${3b^2}/{16a^2}= c/a$ [by (1)]
$3b^2$ = 16ac.
Two numbers whose sum is 6 and the absolute value of whose difference is 8 are the roots of the equation
Answer: (b)
Let α and β are the roots
α + β = 6
α – β = 8
2α = 14
α = 7
β = –1
α + β = 6, α β = –7
The quadratic equation is $x^2$ – 6x – 7 = 0
If α and β are the roots of the quadratic equation $ax^2$ + bx c + = 0 , then the value of $α^2/β + β^2/α$ is
Answer: (b)
Here, α + β = -$b/a$ and αβ = $c/a$
Thus, $α^2/β + β^2/α = {α^3 + β^3}/{αβ}$
= ${(α + β) (α^2 - α β + β^2)}/{αβ}$ …(1)
Now, $(α^2 + β^2 - αβ) = [(α + β)^2 - 2αβ - αβ]$
= $[(α + β)^2 - 3αβ]$
Hence (1) becomes
⇒ ${(α + β)[(α + β)^2 - 3αβ)]}/{αβ} = {{-b}/a[b^2/a^2 - {3c}/a]}/{c/a}$
= ${-b}/c [{b^2 - 3ac}/a^2] = {3abc - b^3}/{a^2c}$
If p and q are the roots of the equation $x^2 – px + q$ = 0, then what are the values of p and q respectively?
Answer: (c)
ibps po prelims 2024 2025 IMPORTANT QUESTION AND ANSWERS
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Top 100+ IBPS PO Prelims Profit and Loss Model MCQ, PDF »
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100+ IBPS Mixture and Alligation MCQ with Solution, PDF »
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IBPS PO Prelims Compound Interest MCQ with Solution, PDF »
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100+ IBPS Number Series Aptitude MCQ with Solution, PDF »
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Top 100+ IBPS Quadratic Equations MCQ with Solution, PDF »
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100+ IBPS PO Prelims Probability Questions Answers, PDF »
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Top IBPS PO Prelims Permutation and Combination Mcq, PDF »
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