Question

find the discriminant.
$8w^2 = 3$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Rewrite to standard quadratic form

$8w^2 - 3 = 0$

Step2: Identify coefficients $a,b,c$

$a=8$, $b=0$, $c=-3$

Step3: Calculate discriminant $\Delta=b^2-4ac$

$\Delta = 0^2 - 4(8)(-3) = 96$

Step4: Analyze discriminant sign

$\Delta=96>0$, so two real solutions.

Answer:

Discriminant: $96$
Number of real solutions: two real solutions