Answer:
a) (x + 5) (x - 5)
b) (x + 5i) (x - 5i)
c) (x + (5i/2)) (x - (5i/2))
d) (x-1)(x-1)
e) x +i√3 +1) (x -i√3+1)
Step-by-step explanation:
To solve this, we will need to factorize each quadratic function making it equal to zero first and then proceeding to find x
a) f(x) = x²-25
x²-25 = 0
⇒(x + 5) (x - 5)
b) f(x)=x²+25
x² + 25 = 0
x²= -25
x = √-25
x = √25i
x = ±5i
⇒(x + 5i) (x - 5i)
c) f(x)=4x²+25
4x²+25 = 0
4x²= -25
x² = -25/4
x = ±√(-25/4)
x = ±(√25i)/2
x = ±5i /2
⇒(x + (5i/2)) (x - (5i/2))
d) f(x)=x²-2x+1
x²-2x+1 = 0
⇒(x - 1)²
e) f(x)=x²-2x+4
x²-2x+4 = 0
x²-2x = -4
x²-2x +1 = -4 +1
x²-2x + 1 = -3
(x-1)² +3 = 0
(x-1)²= -3
x-1 = √-3
x = ±√3i +1
⇒(x +i√3 +1) (x -i√3+1)
The answer and explanation is given in the picture below
I hope it helps.
For the above equation and given zeros of polynomial equation we have;
y=(x+2)(x-3)(x+4)
y=(x^2+2x-3x-6)(x+4)
y=(x^2-x-6)(x+4)
y=(x^3-x^2-6x+4x^2-4x-24)
y=x^3+3x^2-10x-24
Therefore our answer is 3
Hope this helps. Any questions please just ask. Thank you.
Answer:
Here we have the relation:
m = 140*h
Where m is the distance in miles, and h is time in hours.
And we want to complete a table like:
![\left[\begin{array}{ccc}in, h&out, m\\&\\&\\&\\&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C%26%5C%5C%26%5C%5C%26%5C%5C%26%5Cend%7Barray%7D%5Cright%5D)
The way to complete this, is to evaluate the function:
m = 140*h
in different values of h, and then record both values of h and m in the table.
Let's use values of h that increase by 0.5, then:
if h = 0.5
m = 140*0.5 = 70
We have the pair: h = 0.5, m = 70
if h = 1
m = 140*1 = 140
We have the pair: h = 1, m = 140
if h = 1.5
m = 140*1.5 = 210
Then we have the pair h = 1.5, m = 210
if h = 2
m = 140*2 = 280
We have the pair: h = 2, m = 280
Now we can complete the table, and it will be:
![\left[\begin{array}{ccc}in, h&out, m\\0.5&70\\1&140\\1.5&210\\2&280\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Din%2C%20h%26out%2C%20m%5C%5C0.5%2670%5C%5C1%26140%5C%5C1.5%26210%5C%5C2%26280%5Cend%7Barray%7D%5Cright%5D)