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.