Question

Find the number of solutions of the equation 6x2 + 6x + 3 = 0 by using the discriminant

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the standard form of a quadratic equation

`ax^2+bx+c=0`

STEP 2: Write the formula for getting a discriminant

`D=b^2-4ac`

STEP 3: Write the given quadratic equation

`\begin{gathered} 6x^2+6x+3=0 \\ a=6,b=6,c=3 \end{gathered}`

STEP 4: Substitute the values to get the discriminant

`\begin{gathered} D=6^2-4(6)(3) \\ D=36-72=-36 \\ D=-36 \end{gathered}`

STEP 5: Explain the conditions for using the discriminant

If the discriminant is greater than zero, there are two solutions.

If the discriminant is equal to zero, there is one real solution

If the discriminant is less than zero, there are no real solutions

Hence, using the conditions above,

There are no real solutions since the discrimian