Question

How do you find the value of the discriminant and determine the nature of the roots `9n^2-3n-8=-10`?

Answer 1

No real roots.

Explanation:

Solve the quadratic equation:
`f(n) = 9n^2 - 3n - 8 + 10 = 9n^2 - 3n + 2 = 0`
Use the improved quadratic formula (Socratic Search).
`D = d^2 = b^2 - 4ac = 9 - 72 = - 63 < 0`
Since D < 0, there are no real roots. There are 2 imaginary roots.