Quadratic Equation HELP!?

Question

Using the quadratic equation x2 – 4x – 5 = 0, perform the following tasks:
a) Solve by factoring
b)Solve by using the quadratic formula

Answer 1

Solve by factoring:
x^2-4x-5=0
(x+1)(x-5)=0
x=-1 or 5

Solve by quadratic formula:
x=-b±√b^2-4ac/2a
a=1,b=-4,c=-5
x=(4±√(-4)^2-4(1*-5))/2(1)
x=(4±√16+20)/2
x=(4±√36)/2
x=(4±6)/2
x=-1 or 5

Answer 2

Factoring review!
Solve each by factoring
1) x2 + 4x -5 = 0
Solution: factor (x + 5)(x - 1) = 0
Therefore, x = -5 or x = 1
2) (3x - 2)((x + 4) = -11
Solution: Foil first 3x2 + 10x - 8 = -11
Put in correct form 3x2 + 10x + 3 = 0

Completing the square!!
Follow the explanation and sample problem to review completing the square
1) Use completing the square to find the solutions for:
2x2 - 12x - 9 = 0
Solution:
Move the constant to the other side: 2x2 - 12x = 9
Divide by the coefficient of x2 x2 - 6x = 9/2
Take half the coefficient of x and square: x2 - 6x + 9 = 9/2 + 9
Factor the trinomial square: (x - 3)2 = 27/2
Take the square root of both sides:
Simplify the radical:
Isolate for x:

factor (3x + 1)(x + 3) = 0
Solution: x = -1/3 or x = -3
Quadratic Formula
As proved in class the quadratice formula is derived by completing the square. Here is the formula:

If ax2 + bx + c = 0 then the roots of the equation are:


2x2 + 5 = 3x
2x2 - 3x + 5 = 0 (putting in correct form)
a = 2, b = -3 and c = 5 Use the formula:

Answer 3

One common term that appears often is "equations." For many, this is a buzz word that is recognizable as a math term but truly understanding the term may sometime escape people. The two most common equations are linear equations and quadratic equations but, of course, merely giving an equation a name does not necessarily explain what it is. So, a clearer definition of what exactly the two most common equations - linear and quadratic equations - is needed. A linear equation refers to a particular equation that is graphed on a straight line. Additionally, a linear equation possesses on the line one variable that is commonly referred to as "X" and "X" will always be of a degree that is 1 at most. (That is, there are no exponents; but if you are looking for exponents then be patient because we will get to them shortly!) A common example of a linear equation would be 1x + 2 = 3. Clearly, x would equal 1 in this particular example and it can be figured out by merely using a little algebra on the equation to figure out X. 3 minus 2 equals 1. Therefore, X must equal one as 1 x 1 equals one. And, nope, not all linear equations are that easy as they come as complex as 6(x + 3) = 24 (x +0), but the common factor of isolating x to find the answer doesn't change. A quadratic equation is only different from a linear equation in one respect: one or more of the figures is squared. (The word quadratic derives from the Latin word for squared) The common form of a quadratic equation is ax2 + bx + c = 11. In such a equation, if a = 1, b = 2 and c = 3 then X must equal 2. We know this because 2 squared is 4 and 4 x 1 = 4. 2 x 2 = 4. As with a linear equation, there can be more complicated versions of a quadratic equation but just with the simple and complex linear equations basic algebraic operations can yield the correct answer.

Answer 4

x^2-4x-5=0
(x-5)(x+1)=0
x=5 x=-1

a=1 b= -4 c=-5

-4 +/-sqrt of (-4)^2- 4(1)(-5) / 2

-4 +/- 16+20/2
-4+/-36/2
-4+6/2=1
-4-6/2=-5

Answer 5

By factoring: you need two numbers, one positive and one negative, that multiply to -5 and add to -4

That should give you -5 and 1

So

(x-5)(x+1)

With the Quad, a=1, b=-4, c=-5

So

-4+or- root of (16-(-20)
-------------------------------
2

= -4+ or minus 6/2 gives

-4-6/2= -5

and

-4+6/2= 1

There you are. Hope it helped.

Answer 6

a)
x2-5x+x-5=0
x(x-5)+1(x-5)=0
(x-5)(x+1)=0
x-5=0 , x+1=0
x=5 , x=-1

B)
a=1, b= - 4, c= - 5

{-(-4)+or-[(-4)^2-4(1)(-5)]^0.5}
whole divided by 2(1)
(4+or-6 )whole divded by 2
10/2 or -2/2
x=5 or x=-1

hmphhh!