Question

How many solutions per each equation?

Answer 1

These are all quadratic equations

`y = ax^(2) + bx + c`
so you can use the formula

`R = b^(2) - 4ac`
to determine the number of real answers.

If R < 0, there is 0 real solution.
If R = 0, there is 1 real solution.
If R > 0, there are 2 real solutions.

Let me do the first one :

`y = -3x^(2) + x + 12`
You find

`R = 1^(2) - 4 * (-3) * 12 > 0`
Thus this equation has two real solutions.