Answer:
Step-by-step explanation:
Theorm-The Fundamental Theorem of Algebra: If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.
Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.
A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.
As we have seen, factoring a quadratic equation will result in one of three possible situations.
graph 1
The quadratic may have 2 distinct real roots. This graph crosses the
x-axis in two locations. These graphs may open upward or downward.
graph 2
It may appear that the quadratic has only one real root. But, it actually has one repeated root. This graph is tangent to the x-axis in one location (touching once).
graph 3
The quadratic may have two non-real complex roots called a conjugate pair. This graph will not cross or touch the x-axis, but it will have two roots.
Answer:
72
Step-by-step explanation:
The LCM is when you find the lowest factor that 2 or more numbers share.
For 8 and 9,you would just need to keep multiplying each other until you find the same numbers. It would look something like this.
8,16,24,32,40,48,56,64,72..... etc.
9,18,27,36,45,54,63,72,81..... etc.
You can see how they both have the same factor (72), and since that is the lowest factor (which means I can find a lower factor then 72) then your LCM of 8 and 9 should be 72 :)
Answer:
y=2x-2
Step-by-step explanation:
<em>the slope is y/x</em>
the slope is 2 or 2/1
<em>subtract 2 from the y value and 1 from the x value</em>
(3-1,4-2) = (2,2)
<em>keep doing this until you get a 0 in the x value</em>
(2-1,2-2) = (1,0)
<em>1 is your x-intercept</em>
(1-1,0-2) = (0,-2)
-2 is your y intercept.
So now you know your y-intercept and your slope so you can now write your equation.
<em>y=mx+b</em>
<em>m=slope, b=y-intercept</em>
m=2, b=-2
<em>substitute into the equation</em>
y=2x-2
- Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.
(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x: 
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside: 
Now you can rewrite the equation as: 
Now apply zero product property to the factors to solve for x:
<u>The x-intercepts are (1/5 ,0) and (-1,0).</u>
