Question

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

2x² - 6x + 3 = 0

Determine the nature of the roots of the following quadratic equation:

2x² - 6x + 3 = 0

Answer 1

2x² - 6x + 3 = 0

Comparing the given quadratic equation with ax² + bx + c = 0, we get

a = 2, b = -6, c = 3

Discriminant = b² - 4ac

= (-6)² - 4 (2) (3)

= 36 - 24

= 12

As b² - 4ac > 0,

Therefore, distinct real roots exist for this equation

x = `(-b+-b^2-4ac)/(2a)`

= `(-(-6)+-sqrt((-6)^2-4(2)(3)))/(2(2))`

= `(6+-sqrt12)/4`

= `(6+-2sqrt3)/4`

= `(3+-sqrt3)/2`

Therefore, the root are `x=(3+sqrt3)/2 and x = (3-sqrt3)/2`