Question

Solve the following quadratic equation.

3x² − 7x + 5 = 0

Answer 1

Comparing the equation 3x² − 7x + 5 = 0 with ax² +bx + c = 0, we have,

a = 3, b = −7, c = 5

∴ b² – 4ac = (−7)² – 4 × 3 × 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))`

= `(7 ± sqrt(11)"i")/6`

Hence, the roots of the equation are

`(7 + sqrt(11)"i")/6` and `(7 - sqrt(11)"i")/6`.