Question

find the discriminant.
$2p^2 + 9p = -7$
how many real solutions does the equation have?
no real solutions
one real solution
two real solutions

Explanation:

Step1: Rewrite to standard form

$2p^2 + 9p + 7 = 0$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=2$, $b=9$, $c=7$

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 9^2 - 4(2)(7)$
$\Delta = 81 - 56 = 25$

Step4: Analyze discriminant

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

Answer:

Discriminant: $25$
Number of real solutions: two real solutions