Question

Which of the following equations have complex roots?OA. 3x2 - 1 = 6xB. 2x² - 1 = 5xOC. 3x² + 2 = 0OD. 2x + 1 = 7xReset Selection

Answer 1

`C.\text{ }3x^2+2=0`

Step-by-step explanation

We want to identify the equations that have complex roots.

For an equation to have complex roots, the following condition must be satisfied:

`b^2-4ac<0`

where a = leading coefficient

b = coefficient of x

c = constant term

Let us test for each equation.

For option A:

`\begin{gathered} 3x^2-1=6x \\ \\ 3x^2-6x-1=0 \\ \\ a=3,\text{ }b=-6,\text{ }c=-1 \\ \\ (-6)^2-(4*3*-1) \\ \\ 36+12 \\ \\ 48 \end{gathered}`

Since this value is not less than 0, it does not have complex roots.

For option B:

`\begin{gathered} 2x^2-1=5x \\ \\ 2x^2-5x-1=0 \\ \\ a=2,\text{ }b=-5,\text{ }c=-1 \\ \\ (-5)^2-(4*2*-1) \\ \\ 25+8 \\ \\ 33 \end{gathered}`

It does not have complex roots.

For option C:

`\begin{gathered} 3x^2+2=0 \\ \\ a=3,\text{ }b=0,\text{ }c=2 \\ \\ (0)^2-(4*3*2) \\ \\ 0-24 \\ \\ -24 \end{gathered}`

Since this value is less than 0, it has complex roots.

Therefore, the correct option is option C.