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