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:

`6x^2-x-2=0`

To find:

The nature of the solutions by using the discriminant.

Solution:

If a quadratic equation is
`ax^2+bx+c=0`, then its discriminant is:

`D=b^2-4ac`

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,

`6x^2-x-2=0`

Here,
`a=6,b=-1,c=-2`. So, the value of the discriminant is:

`D=(-1)^2-4(6)(-2)`

`D=1+48`

`D=49`

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

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