quadratic equations Model Questions & Answers, Practice Test for ibps so prelims 2023
ibps so prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Quadratic Equations
If one root of the equation ${x^2}/a + x/b + 1/c$ = 0 is reciprocal of the other, then which one of the following is correct ?
Answer: (c)
Given equation,
${x^2}/a + x/b + 1/c$ = 0
$bcx^2$ + acx + ab = 0
Let roots are α and $1/{α}$
Product of roots = α . $1/{α} = {ab}/{bc} ⇒ 1 = a/c$
⇒ ∴ c = a
If (2x - 3y < 7) and (x + 6y < 11), then which one of the following is correct ?
Answer: (b)
Given,
2x - 3y < 7
and x + 6y < 11
On adding equations (i) and (ii),
3x + 3y < 18
⇒ x + y < 6
What is the condition that the equation $ax^2$ + bx + c = 0, where a ≠ 0 has both the roots positive ?
Answer: (c)
a and c have the same sign opposite to that of b.
Two numbers p and q are such that the quadratic equation $px^2$ + 3x + 2q = 0 has - 6 as the sum and the product of the roots. What is the value of (p - q) ?
Answer: (a)
$Px^2 + 3x + 2q$ = 0
Let two roots are α and β
then, α + β = -6 = ${-3}/P$
∴ P = $1/2$
α . β = -6 = ${2q}/P$
$q/p$ = -3
q = -3p = - 3 × $1/2$ = - 1.5
(p - q) = $(1/2 + 1.5)$ = 2
The quadratic equation whose roots are 3 and -1, is
Answer: (b)
Here, given roots of equation are 3 and -1.
So, expression can be written as
(x - 3) (x + 1) = 0
= $x^2$ - 3x + x - 3 = 0
= $x^2$ - 2x - 3 = 0
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