Question

find the discriminant.
$-1 = -3s^{2}$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Rewrite to standard quadratic form

Rearrange $-1 = -3s^2$ to $3s^2 - 1 = 0$, so $a=3$, $b=0$, $c=-1$.

Step2: Calculate discriminant

Use discriminant formula $\Delta = b^2 - 4ac$.
$\Delta = 0^2 - 4(3)(-1) = 12$

Step3: Analyze discriminant sign

Since $\Delta = 12 > 0$, there are two real solutions.

Answer:

Discriminant: $12$
Number of real solutions: two real solutions