Determine the nature of the roots of the equation 2y2 + 5y – 3 = 0 from its discriminant.

Solution: Comparing the given equation 2y2 + 5 y – 3 = 0 with the standard quadratic equation ax2 + bx + c = 0 we get,

a = 2,   b = 5 and c = - 3

Discriminant ∆  = b2 – 4ac

∴ ∆ = 52 – 4 (2) (-3)

∴ ∆ = 25 + 24

∴ ∆  = 49

∵ ∆ > 0

∴ the nature of the root is real and unequal.