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Solve the following quadratic equation: 3x2 – 7x + 5 = 0 - Mathematics and Statistics

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Sum

Solve the following quadratic equation:

3x2 – 7x + 5 = 0

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Solution

Given equation is 3x2 – 7x + 5 = 0
Comparing with ax2 + bx + c = 0, we get
a = 3, b = – 7, c = 5
Discriminant = b2 – 4ac

= (– 7)2 – 4 x 3 x 5

= 49 – 60 = – 11 < 0
So, the given equation has complex roots.
These roots are given by

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

= `(- (- 7) ± sqrt( - 11))/(2(3))`

∴ x = `(7 ± sqrt(11)"i")/6`

∴ the roots of the given equation are `(7 + sqrt(11)"i")/6 and (7 - sqrt(11)"i")/6`.

Concept: Solution of a Quadratic Equation in Complex Number System
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.2 | Q 2. (iii) | Page 40
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