General Basic Stats Questions

Ok, so Ive started Maths with Statistics at my college along with Pure Maths. I havent had a lesson in several months so Ive forgotten a lot of things so if you could just help me with some question I have an explain how you got those questions that would be nice:)

1.I have to solve an equation of f(x)=0 with:
x²-3x+1 and 2x²-3x+1


2.I have to write the following equations in the form of: (x+or-a)²+or-b

x²+2x+5 and -x²-4x. Is x²+2x+5 written as (x+1)²+5?


3. A little more meaty. I need ot calculate the discriminant of the quadratic functions below and determine if the equation f(x)=0 has two, one or no real solutions. I dont understand what real solutions are. I have equations like x²+2x+1 and x²-3x+3 and asking if they are discriminant and then the whole bit about one, two or no real solutions? What do I do? :(

These are Pure questions

1.

2x² - 3x + 1 = 0
(2x - 1)(x - 1) = 0
x = 1/2 or x = 1

x² - 3x + 1 = 0

Can't factorise this one, complete the square

(x - 3/2)² - (3/2)² + 1 = 0

(x - 3/2)² - (9/4) + 1 = 0

(x - 3/2)² - (5/4) = 0

(x - 3/2)² = (5/4)

(x - 3/2) = (\sqrt{5}/2) or (x - 3/2) = -(\sqrt{5}/2)

x = 3/2 + (\sqrt{5}/2) or x = 3/2 - (\sqrt{5}/2)

2

x² + 2x + 5

(x + 1)² - 1² + 5

(x + 1)² - 1 + 5

(x + 1)² + 4

Other one

-x² - 4x

-[x² + 4x]

-[(x + 2)² - 2²]

-[(x + 2)² - 4]

-(x + 2)² + 4

3

Real numbers is the set of all numbers that you have ever come across

Whole numbers, fractions and irrational numbers (including negatives)

The discriminant of a quadratic ax² + bx + c = 0 is b² - 4ac

If the discriminant is positive then there are 2 real solutions

If the discriminant is zero then there is 1 real solution

If the discriminant is negative then there are no real solutions

The discriminant comes from the quadratic formula which is why it works like this