Question

Without solving, comment upon the nature of roots of the following equations :

`x^2 + 2sqrt3x - 9 = 0`

Answer 1

`x^2 + 2sqrt3x - 9 = 0`

`a = 1, b = 2sqrt3 and c= -9`

∴ Discriminant = `b^2 - 4ac`

`= (2sqrt3)^2 - 4(1)(-9)`

= 12 + 36 = 48

Since 48 is not perfect square, roots are irrational

Since D > 0, then equation has two irrational and unequal roots.