MATHSWATCH
1 answer:
You might be interested in
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.
Answer:
Min = 0; Q₁ = 0; Median = 2; Q₃ = 2; Max = 8
Step-by-step explanation:
Assume that your sorted data are
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8
1. Minimum
Min = 0
2. Median
The median is the middle value in a sorted data set. There are 25 items, so the median is the 13th item.
Median = 2
3. First quartile
Q₁ is the median of the lower half of the data set.
The median of 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2 is 0.
Q₁ = 0
4. Third quartile
Q₃ is the median of the upper half of the data set.
The median of 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8 is 3.
Q₃ = 3
5. Maximum
Max = 8
