Question

Determine the nature of roots of the following quadratic equation.

m² + 2m + 9 = 0

Answer 1

m² + 2m + 9 = 0
Comparing the given equation with the quadratic equation \[a x^2 + bx + c = 0\] \[a = 1, b = 2, c = 9\] Discriminant,  

\[\bigtriangleup = b^2 - 4ac = \left( 2 \right)^2 - 4 \times 1 \times 9 = 4 - 36 = - 32\] 

Since the discriminant < 0 so, the roots of the given quadratic equation are not real.