# How do you find the nature of the roots using the discriminant given 2x^2 + 7x - 3 = 0?

The roots are real: $0.386 , - 3.886$
Here in the quadratic equation of form ax^2+bx+c; a=2 ; b=7;c=-3 :.Discriminant $d = {b}^{2} - 4 a c = {7}^{2} - \left(4 \cdot 2 \cdot \left(- 3\right)\right) = 73$ since $d > 0$ the roots are real. Roots$= \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} \therefore$root1$= \frac{- 7 + \sqrt{73}}{4} = 0.386$ and root2 $= \frac{- 7 - \sqrt{73}}{4} = - 3.886$[Ans]