Question

1. find the discriminant.

$4p = -7p^2 + 3$

1. how many real solutions does the equation have?

no real solutions
one real solution
two real solutions

Explanation:

Step1: Rearrange to standard quadratic form

$7p^2 + 4p - 3 = 0$

Step2: Identify a, b, c values

$a=7,\ b=4,\ c=-3$

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 4^2 - 4(7)(-3)$
$\Delta = 16 + 84 = 100$

Step4: Analyze discriminant sign

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

Answer:

Discriminant: $100$
Number of real solutions: two real solutions