Learning Task 3. Do the following: A. Characterize the roots of the following quadratic equations using the
discriminant.
1. x2 + 4x + 3 = 0
4 4x2 - 4x + 1 = 0
2. x2 - 5x + 4 = 0
5. 2x2 + 6x + 3 = 0
3. x2 + 7 = 0
B. Complete the table.
Equation
a
b
Roots
X1 + X2
X
XI. X2
X2
x2 + 5x + 4 = 0
x2 - 6x-27 = 0
x2 - 25 = 0
x2 + 10x + 25 = 0
2x2 - 5x + 3 = 0

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −5 0 −1 1 3 g(x) g(x) = 2x − 7 part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) part b: which function has a greater y-intercept? justify your answer. (4 points)

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.