Answer:
The system of equations has two real roots
Step-by-step explanation:
y = x² + 3x + 4 ------------(I)
y - x = 7 ------------------------(II)
y = 7 +x
Substitute y = 7 + x in equation (I),
7 + x = x² + 3x + 4
0 = x² + 3x + 4 - x - 7
0 = x² + 3x - x + 4 - 7
Combine like terms,
0 = x² + 2x - 3
x² + 2x - 3 = 0
a = 1; b = 2; c = -3
Discriminant = b² - 4ac
= 2² - 4*1*(-3)
= 4 + 12
= 16
System of equations has two real roots as discriminant is greater than 0.