Quadratic Equations Mcq Model Questions & Answers, Practice Test for ibps po mains 2024 2025

ibps po mains 2024 2025 SYLLABUS WISE SUBJECTS MCQs

Number System

Simplification

Ratio & Proportion

Percentage

Time & Work

Time & Distance

Mensuration

Data Sufficiency

Average

Profit & Loss

Alligation & Mixtures

Compound Interest

Number Series

Linear Equations

Quadratic Equations

Probability

Permutations & Combination

Click To More Exercise For Quadratic Equations
Question :1

  1. $x^2$ + 91 = 20x
  2. $10y^2$- 29y+ 21 = 0

Answer: (c)

Question :2

  1. $x^2$ + x - 6 = 0
  2. $2y^2$ - 13y + 21 = 0

Answer: (c)

Question :3

The roots of the equation $2√x + 2x^{-1/2}$ = 5 can be found by solving

Answer: (a)

$2√x + 2/√x$ = 5

2x + 2 = 5$√x$

⇒ $4x^2$ + 8x + 4 = 25x

⇒ $4x^2$ – 17x + 4 = 0

Question :4

The discriminant of $ax^2 - 2√{2x} + c$ = 0 with a, c are real constants is zero. The roots must be

Answer: (a)

$ax^2 - 2√{2x}$ + c = 0

$(2√2)^2$ - 4ac = 0

4ac = 8

ac = 2

c = $2/a$

Let α, β be the roots.

α + β ${2√2}/a$ , α β = $c/a = 2/a^2$

$(α – β)^2 = (α + β)^2 – 4α β$

= $8/a^2 - 8/a^2 = 0$

α = β

So, α = β = $√2/a$

Hence the roots are real and equal.

Question :5

If the roots of the equation $(a^2 + b^2 ) x^2 – 2(ac + bd) x + (c^2 + d^2)$ = 0 are equal, then which of the following is true?

Answer: (b)

Solve this by assuming each option to be true and then check whether the given expression has equal roots for the option under check.

Thus, if we check for option (b).

ad = bc.

We assume a = 6, d = 4 b = 12 c = 2 (any set of values that satisfies ad = bc)

Then $(a^2 + b^2)x^2 – 2(ac + bc)x + (c^2 + d^2)$ = 0

$180x^2$ – 120x + 20 = 0

We can see that this has equal roots.

Thus, option (b) is a possible answer. The same way if we check for a, c and d we see that none of them gives us equal roots and can be rejected.

Click To More Exercise For Quadratic Equations
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Quadratic Equations ibps po mains 2024 2025 question answer with explanation PDF
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