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Test: Quadratic Equations - Commerce MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Quadratic Equations

Test: Quadratic Equations for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The Test: Quadratic Equations questions and answers have been prepared according to the Commerce exam syllabus.The Test: Quadratic Equations MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Quadratic Equations below.
Solutions of Test: Quadratic Equations questions in English are available as part of our Mathematics (Maths) Class 11 for Commerce & Test: Quadratic Equations solutions in Hindi for Mathematics (Maths) Class 11 course. Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. Attempt Test: Quadratic Equations | 10 questions in 10 minutes | Mock test for Commerce preparation | Free important questions MCQ to study Mathematics (Maths) Class 11 for Commerce Exam | Download free PDF with solutions
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Test: Quadratic Equations - Question 1

Solve the quadratic equation x2 – ix + 6 = 0

Detailed Solution for Test: Quadratic Equations - Question 1

x2 - ix + 6 = 0
x2 - 3ix + 2ix - 6i2 = 0    { i2 = -1}
x(x-3i) + 2i(x-3i) = 0
(x+2i) (x-3i) = 0
x = -2i, 3i 

Test: Quadratic Equations - Question 2

 so the least integral value of n is

Detailed Solution for Test: Quadratic Equations - Question 2

{(1 + i)/(1 - i)}n = 1
multiply (1 + i) numerator as well as denominator .
{(1 + i)(1 + i)/(1 - i)(1 + i)}n = 1
{(1 + i)²/(1² - (i)²)}n = 1
{(1 + i² +2i)/2 }n = 1
{(2i)/2}n = 1
{i}n = 1
we know, i4n = 1 where , n is an integer.
so, n = 4n where n is an integers
e.g n = 4 { because least positive integer 1 }
hence, n = 4

Test: Quadratic Equations - Question 3

Solve the quadratic equation ix2 – 3x – 2i = 0

Detailed Solution for Test: Quadratic Equations - Question 3

Test: Quadratic Equations - Question 4

Find the roots of the quadratic equation: x2 + 2x - 15 = 0?

Detailed Solution for Test: Quadratic Equations - Question 4

x2 + 5x - 3x - 15 = 0
x(x + 5) - 3(x + 5) = 0
(x - 3)(x + 5) = 0
⇒ x = 3 or x = -5.

Test: Quadratic Equations - Question 5

Solve the quadratic equation x2 +1 = 0

Detailed Solution for Test: Quadratic Equations - Question 5

Test: Quadratic Equations - Question 6

The solution of the quadratic equation: 2x2 + 3ix + 2 = 0

Detailed Solution for Test: Quadratic Equations - Question 6

2x2 + 3ix + 2 = 0
Using quadratic equation;
we know, x = (-b ± √b2 - 4ac)/2a
x =  [-3i ± √(3i)2 - 4x2x2]/2x2
= -3i ± √-25/4
= i(-3±5)/4
x = i/2, -2i

Test: Quadratic Equations - Question 7

The solution of the quadratic equation : 2x2 – 4x + 3 = 0

Detailed Solution for Test: Quadratic Equations - Question 7

2x2 - 4x + 3 = 0
x = [-(-4) +- (√16-24)]/2(2)
x = (4 +- i√8)/4
x = (4 +- 2i√2)/(2 * √2 * √2)
x = 2(2 +- i√2)/(2 * √2 * √2)
x = 1 +- i/√2

Test: Quadratic Equations - Question 8

If one of the root of a quadratic equation with rational coefficients is rational, then other root must be

Detailed Solution for Test: Quadratic Equations - Question 8

Also, αβ = r/p, which is also rational. α + β = (a+√b) + (a-√b) = 2a, a rational number and, αβ = (a+√b)(a-√b) = a² - b, a rational number. So, the other root of a quadratic equation having the one root as (a+√b) is (a-√b), where a and b are rational numbers.

Test: Quadratic Equations - Question 9

Detailed Solution for Test: Quadratic Equations - Question 9

Test: Quadratic Equations - Question 10

Solve the quadratic equation 9x2 + 16 = 0

Detailed Solution for Test: Quadratic Equations - Question 10

9x2 + 16 = 0
9x2 = -16
x2 = -16/9
x = ± 4/3 i

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