quadratic equations Model Questions & Answers, Practice Test for ibps so prelims 2023

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

Answer: (b)

Given,

2x - 3y < 7

and x + 6y < 11

On adding equations (i) and (ii),

3x + 3y < 18

⇒ x + y < 6

Answer: (c)

a and c have the same sign opposite to that of b.

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

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