Question

Question 16) Find the number of solutions of theequation 6^2+ 6x + 3 = 0 by using the discriminant.(1 solution, 2 solutions, or no real solutions)

Answer 1

We are given the following equation:

`6x^2+6x+3=0`

This is an equation of the form:

`ax^2+bx+c=0`

The discriminant of the equation is:

`d=b^2-4ac`

We have 3 possible cases:

`d<0`

There are two imaginary solutions

`d=0`

one real solution

`d>0`

Two real solutions.

Replacing the values:

`d=(6)^2-4(6)(3)`

Solving the operations:

`\begin{gathered} d=36-72 \\ d=-36 \end{gathered}`

We have:

`d<0`

This means that we have 2 imaginary solutions.