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Question
Solve the following quadratic equation:
3x2 – 7x + 5 = 0
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`.
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