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

ibps clerk prelims 2023 SYLLABUS WISE SUBJECTS MCQs

Ratio & Proportion

Percentages

Profit & Loss

Time & Work

Time & Distance

Simple Interest & Compound Interest

Mensuration: Area & Volumes

Algebraic Expressions

Trigonometric Ratios & Identity

Linear Equations

Quadratic Equations

Logarithm

Click To More Exercise For Quadratic Equations
Question :21

The equation $x^2$ + px + q = 0 has roots equal to p and q where q ≠ 0. What are the values of p and q respectively ?

Answer: (d)

p and q are roots of

$x^2 + px + q = 0$

⇒ p + q = - p and pq = q

⇒ pq - q = 0

⇒ q (p - 1) = 0 ⇒ (p - 1) = 0 ⇒ p = 1

Adding p in equation p + q = - p

⇒ 1 + q = -1

⇒ q = -2

Question :22

If the roots of the equation $Ax^2$ + Bx + C = 0 are - 1 and 1, then which one of the following is correct?

Answer: (a)

Given equation,

$Ax^2$ + Bx + C = 0

Since, the given roots are - 1 and 1.

∴ Sum of roots = -1 + 1 = 0

and Products of roots = 1 × (-1) = -1

Standard equation is

$x^2$ - (Sum pf roots)x + Product of roots = 0

On comparing with above equation from equation (i),

$x^2 + B/A x + C/A$ = 0

∴ $C/A$ = Product of roots ⇒ C = -A

So, A and C are of opposite signs.

Question :23

A quadratic polynomial $ax^2$ + bx + c is such that when it is divided by x, (x - 1) and (x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a + b) ?

Answer: (d)

Question :24

Which one is one of the factors of $x^2 + 1/{x^2} + 8 (x + 1/x) + 14$ ?

Answer: (a)

We know that

$(x + 1/x)^2 - 2 = x^2 + 1/{x^2}$

Now, put this value in expression

$(x + 1/x)^2 - 2 + 8(x + 1/x) + 14$

⇒ $(x + 1/x)^2 + 8 (x + 1/x) + 12$

⇓ ⇓

6 + 2 6 × 2

So factor of this expression = $(x + 1/x + 6)$

Question :25

If sum as well as product of roots of a quadratic equation is 9, then what is the equation?

Answer: (c)

Let roots of equation are α and β

α + β = 9 and α β = 9

Now, equation is

$x^2$ - (α + β)x + (α β) = 0

⇒ $x^2$ - 9x + 9 = 0

Click To More Exercise For Quadratic Equations
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