Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation = 
For real roots,
p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.
The solution to the quadratic equation are option C) x= -5 and option E) x=3.
<u>Step-by-step explanation</u>:
The given quadratic equation is x²+2x-15 = 0.
Using the factorization method,
- product of the roots should be -15.
- Sum of the roots should be 2.
⇒ -15 = 5 
-3
⇒ 2 = 5+(-3)
(x+5)(x-3) = 0
Therefore, x = -5 and x = 3
Answer:
Step-by-step explanation:
total cost = c
students = s
cost = 7
c = s*7
independent is s
dependent is c
Answer:
5,750-2,480=3270
Step-by-step explanation:
5,750-2,480=3270
This is a typical algebra problem pretending to be geometry. The two indicated angles are supplementary, adding to 180 degrees, precisely when the lines are parallel.
It's not really indicated, but the 8 and the 2 are in units of degrees.
6x + 8 + 4x + 2 = 180
10x = 170
x = 17 degrees
