Test: Quadratic Equations - JEE MCQ

Test: Quadratic Equations - JEE MCQ

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10 Questions MCQ Test - Test: Quadratic Equations

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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

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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
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