quadratic equations mcq pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024
ibps rrb so officer sclae 2 3 single exam 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Lcm & Hcf
Ratio & Proportion
Percentage
Time & Work
Mensuration
Advance Math
Trigonometric Ratios & Identities
Average
Profit & Loss
Alligation & Mixtures
Compound Interest
Linear Equations
Quadratic Equations
The roots of the equation $ax^2$ + bx + c = 0 will be reciprocal if
Answer: (a)
Since roots are reciprocal, product of the roots = 1 ⇒ $c/a$ = 1
⇒ c = a.
If the roots of the quadratic equation $3x^2 – 5x + p$ = 0 are real and unequal, then which one of the following is correct?
Answer: (b)
The given equation is,
$3x^2$ – 5x + p = 0
We have, a = 3, b = – 5, c = p
D = $b^2$ – 4ac = 25 – 12 p
For Real and unequal, D > 0
∴ 25 – 12 p > 0
⇒ 25 > 12 p ⇒ p < $25/12$
The condition that both the roots of quadratic equation $ax^2$ + bx + c = 0 are positive is
Answer: (c)
For both the roots: (α, β) to be positive
α + β > 0 and α β> 0
⇒ ${- b}/a$ > 0 and $c/a$ > 0
i.e., b and a are of opposite sign and c and a are of same sign.
If x = 3 + 2$√2$, then ${x^6 + x^4 + x^2 + 1}/x^3$ is equal to
Answer: (d)
We have, x = 3 + 2$√2$
$1/x = 1/{3 + 2√2} × {3 - 2√2}/{3 - 2√2} = 3 - 2√2$
$x + 1/x = 6$
${x^6 + x^4 + x^2 + 1}/x^3 = x^3 + x + 1/x + 1/x^3$
= $(x^3 + 1/x^3) + (x + 1/x)$
= $(x + 1/x) (x^2 + 1/x^2 - 1) + (x + 1/x)$
= $(x + 1/x) [(x + 1/x)^2 - 3] + (x + 1/x)$
= 6$[6^2 – 3]$ + 6 = 198 + 6 = 204
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