SOLUTION: Using the quadratic equation x3 - 4x + 3 = 0 1. Solve by factoring 2. Solve by completing the square 3. Solve by using the quadratic formula Can someone help me with this?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Using the quadratic equation x3 - 4x + 3 = 0 1. Solve by factoring 2. Solve by completing the square 3. Solve by using the quadratic formula Can someone help me with this?       Log On


   

Question 27658: Using the quadratic equation x3 - 4x + 3 = 0
1. Solve by factoring
2. Solve by completing the square
3. Solve by using the quadratic formula
Can someone help me with this?
Thanks so much
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
I presume you mean: x%5E2-4x%2B3=0
To solve by factoring, you need to find two numbers that multiply together to get the last term (3) and add together to get (-4). The only two numbers that fit the are -1 and -3. So you write:
%28x-1%29%28x-3%29=0 Because if either term (x+1 or x+3) was 0 then their product must be zero, the two numbers that would work for x are 1 & 3 (1-1 or 3-3 both equal 0).
Completing the square: To do this you need to rearrange terms to create a square polynomial. A square polynomial is a polynomial in the form:
ax%5E2%2B2ab%2Bb%5E2 which can be factored to the squared binomial %28ax%2Bb%29%5E2
x%5E2-4x%2B3=0 I find it easiest to move the constant (3) over to the other side first.
x%5E2-4x=-3 Now we need to know what number can be added to x%5E2-4x to make it a square polynomial. To do that we divide the middle term (4) by 2 and then square the answer:
%284%2F2%29%5E2=2So we need to add 4 to both sides to get the polynomial to square:
x%5E2-4x%2B4=-3%2B4The left side factors to:
%28x-2%29%5E2=1Taking the square root of each side:
x-2=+%2B-1Add two to both sides:
x=2+%2B-1 This gives answers of 2-1=1 and 2+1=3 our answers, 1 & 3.
Quadratic formula is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ for ax%5E2%2Bbx%2Bc
x%5E2-4x%2B3=0 a=1, b=-4, c=3
x+=+%28-%28-4%29+%2B-+sqrt%28%28-4%29%5E2-4%2A1%2A3%29%29%2F%282%2A1%29
x+=+%284+%2B-+sqrt%2816-12%29%29%2F2
x+=+%284+%2B-+sqrt%284%29%29%2F2
x+=+2%282+%2B-+1%29%2F2
x+=+2+%2B-+1
Again we get answers of x = 3 & 1.
Graphically (not that you asked) it would look like:
+graph+%28300%2C+200%2C+-2%2C+6%2C+-3%2C+5%2C+x%5E2-4x%2B3%29
And you can see that the graph crosses the x axis (y=0) at (1, 0) and (3, 0)