Question

Determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve. 6x^2-x-2=0

Answer 1

Given:

The quadratic equation is:

To find:

The nature of the solutions by using the discriminant.

Solution:

If a quadratic equation is
, then its discriminant is:

If D<0, then both roots are complex.

If D=0, then both roots are real and equal.

If D>0, then both roots are real and distinct.

We have,

Here,
. So, the value of the discriminant is:

Since
, then both roots are real and distinct.

Hence, the discriminant of the given quadratic equation is 49 and both roots are real and distinct.