Question

what is the nature of roots of the quadratic equation for 5x²-2x-3=0?

Answer 1

D=b^2 - 4ac
D=4 + 60=64
Since D>0 roots are real and distinct

Answer 2

To find out the nature of roots of an equation of the form ax^2+bx+c=0, you must calculate the determinant d.

Now d = b^2-4ac

If d>0 roots are real and distinct
If d=0 roots are real and equal
If d<0 roots are imaginary.


So from the above equation,
a=5, b= - 2 and c= - 3

Therefore d = (-2)^2-4*5*(-3) = 64

Since d>0 roots are real and distinct.