BRAINLIEST, 5 STARS AND THANKS IF ANSWERED CORRECTLY. How many real solutions does the equation 2p^2 + 9p - 7 = 0 have?

A. 0
B. 1
C. 2
D. 3

C

Step-by-step explanation:

Determine the nature of the solutions using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct solutions

• If b² - 4ac = 0 then 2 real and equal solutions

• If b² - 4ac < 0 then no real solutions\

Given

2p² + 9p - 7

with a = 2, b = 9, c = - 7 , then

b² - 4ac = 9² - (4 × 2 × - 7) = 81 +56 = 137

Since b² - 4ac > 0 then there are 2 real solutions → C

C. 2

Step-by-step explanation:

2p² + 9p - 7 = 0

p = {-9±√((9²)-(4*2*-7))} / (2*2)

p = {-9±√(81+56)} / 4

p = {-9±√137} / 4

p = {-9±11.7} / 4

p₁ = {-9-11.7} / 4 = -20.7/4 = -4.55   aprox.

p₂ = {-9+11.7} / 4 = 2.7/4 = 0.67     aprox.

This equation have 2 real solutions:

-4.55   aprox.

0.67      aprox.