Question

Find, using the quadratic formula, the roots of the following quadratic equations, if they exist

3x² – 5x + 2 = 0

Answer 1

Given quadratic equation is 3x² – 5x + 2 = 0

D = b² – 4ac

= (–5)² – 4(3)(2)

= 25 – 24

= 1

Since D > 0, the roots of the given quadratic equation are real and distinct.

Using quadratic formula, we have

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

`=> x = (5 ± sqrt((-5)^2 - 4(3)(2)))/(2(3)`

`=> x = (5 ± sqrt(25 - 24))/6`

`=> x = (5 ± 1)/6`

`=> x = (5 + 1)/6` or `x = (5 - 1)/6`

`=> x = 6/6` or `x = 4/6`

`=> x = 1` or `x = 2/3`