Solve the following quadratic equation: x2 + 4ix – 4 = 0 - Mathematics and Statistics

Question

Solve the following quadratic equation:

x² + 4ix – 4 = 0

Sum

Solution

Given equation is x² + 4ix – 4 = 0
Comparing with ax² + bx + c = 0, we get
a = 1, b = 4i, c = – 4
Discriminant = b² – 4ac
= (4i)² – 4 x 1 x – 4
= 16i² + 16
= – 16 + 16 ...[∵ i² = – 1]
= 0
So, the given equation has equal roots.
These roots are given by

x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`

= `(-4"i" +- sqrt(0))/(2(1)`

= `(-4"i")/2`

∴ x = – 2i
∴ the roots of the given equation are – 2i and – 2i.

shaalaa.com

Solution of a Quadratic Equation in Complex Number System

Is there an error in this question or solution?

Q 3) iii)Q 3) ii)Q 3) iv)

Chapter 3: Complex Numbers - EXERCISE 3.2 [Page 40]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 11 Maharashtra State Board

Chapter 3 Complex Numbers
EXERCISE 3.2 | Q 3) iii) | Page 40

RELATED QUESTIONS

Find the values of x and y which satisfy the following equations (x, y ∈ R):

`(x + 1)/(1 + "i") + (y - 1)/(1 - "i")` = i

Solve the following quadratic equation:

`2x^2 - sqrt(3) x + 1` = 0

Solve the following quadratic equation:

3x² – 7x + 5 = 0

Solve the following quadratic equation:

x² – 4x + 13 = 0

Solve the following quadratic equation:

x² + 3ix + 10 = 0

Solve the following quadratic equation:

`x^2 - (3 sqrt(2) + 2"i") x + 6 sqrt(2)"i"` = 0

Solve the following quadratic equation:

(2 + i) x² – (5 – i) x + 2(1 – i) = 0

Solve the following equation for x, y ∈ R:

(4 – 5i) x + (2 + 3i) y = 10 – 7i