Question

2. How many real number solutions are there to the equation 0 =-3x2 + x - 4?

Answer 1

For this case we have the following quadratic equation:

`-3x ^ 2 + x-4 = 0`

Where:

`a = -3\\b = 1\\c = -4`

By definition, the discriminant of a quadratic equation is given by:

`d = b ^ 2-4 (a) (c)`

We have to:

`d> 0:` Two different real roots

`d <0:`Two different complex roots

`d = 0:` Two equal real roots

Substituting the values we have:

`d = 1 ^ 2-4 (-3) (- 4)\\d = 1-48\\d = -47`

So, we have two different complex roots

Answer:

Two different complex roots