Solve the following quadratic equation: 8x2 + 2x + 1 = 0 - Mathematics and Statistics

Solve the following quadratic equation:

8x² + 2x + 1 = 0

Sum

Given equation is 8x² + 2x + 1 = 0

Comparing with ax² + bx + c = 0, we get

a = 8, b = 2, c = 1

Discriminant = b² – 4ac

= (2)² – 4 × 8 × 1

= 4 – 32

= – 28 < 0

So, the given equation has complex roots.

These roots are given by

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

= `(-2 +- sqrt(-28))/(2(8)`

= `(-2 ± 2sqrt(7)"i")/16`

∴ x = `(-1 ± sqrt(7)"i")/8`

∴ The roots of the given equation are `(-1 + sqrt(7)"i")/8 and (-1 - sqrt(7)"i")/8`.

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Solution of a Quadratic Equation in Complex Number System

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

Chapter 3 Complex Numbers
EXERCISE 3.2 | Q 2) i) | Page 40

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Solve the following quadratic equations.

`8x^2+2x+1=0`