Solve the following quadratic equation: 2x2-3 x+1 = 0 - Mathematics and Statistics

Solve the following quadratic equation:

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

बेरीज

Given equation is `2x^2 - sqrt(3) x + 1` = 0
Comparing with ax² + bx + c = 0, we get
a = 2, b = `-sqrt(3)`, c = 1
Discriminant = b² – 4ac

= `(-sqrt(3))^2 - 4 xx 2 xx 1`

= 3 – 8 = – 5 < 0
So, the given equation has complex roots.
These roots are given by

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

= `(- - sqrt(3) +- sqrt(-5))/(2(2))`

∴ x = `(sqrt(3) ± sqrt(5)"i")/4`

∴ the roots of the given equation are

`(sqrt(3) + sqrt(5)"i")/4 and (sqrt(3) - sqrt(5)"i")/4`.

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Solution of a Quadratic Equation in Complex Number System

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पाठ 3: Complex Numbers - EXERCISE 3.2 [पृष्ठ ४०]

पाठ 3 Complex Numbers
EXERCISE 3.2 | Q 2) ii) | पृष्ठ ४०

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(x + iy)(5 + 6i) = 2 + 3i