Solve the equation 5x - x² = 0?

x (5 - x) = 0
x = 0 , x = 5

OR

x² - 5x = 0
x = [ 5 ± √ (25) ] / 2
x = [ 5 ± 5 ] / 2
x = 0 , x = 5 (as above)

Question Number 1 :
For this equation -x^2 + 5*x = 0 , answer the following questions :
A. Calculate the Determinant ! Explain what it means !
B. Calculate the Roots ( x1 and x2 ) !
C. Use factorization to find the root of the equation !

Answer Number 1 :
The equation -x^2 + 5*x = 0 is already in a*x^2+b*x+c=0 form.
So we can imply that the value of a = -1, b = 5, c = 0.

1A. Calculate the Determinant ! Explain what it means !
The formula Determinant = b^2-4*a*c is useful to solve this problem.
Since the value of a = -1, b = 5 and c = 0 are known,
the value of a and b inside Determinant = b^2-4*a*c, can be subtituted using the values we know.
So Determinant = (5)^2 - 4 * (-1)*(0)
Which is the same as Determinant = 25+0
We get following answer : Determinant = 25
Positive Determinant value, means that f(x) = -x^2 + 5*x is going to intersect x axis in two points.

1B. Calculate the Roots ( x1 and x2 ) !
By using abc formula the value of x is both
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
As we know that a = -1, b = 5 and c = 0,
then the value a,b and c in the abc formula, can be subtituted.
So x1 = (-(5) + sqrt( (5)^2 - 4 * (-1)*(0)))/(2*-1) and x2 = (-(5) - sqrt( (5)^2 - 4 * (-1)*(0)))/(2*-1)
Which is the same as x1 = ( -5 + sqrt( 25+0))/(-2) and x2 = ( -5 - sqrt( 25+0))/(-2)
Which is can be turned into x1 = ( -5 + sqrt( 25))/(-2) and x2 = ( -5 - sqrt( 25))/(-2)
It imply that x1 = ( -5 + 5 )/(-2) and x2 = ( -5 - 5 )/(-2)
We get following answers x1 = 0 and x2 = 5

1C. Use factorization to find the root of the equation !
-x^2 + 5*x = 0
<=> ( x ) * ( x - 5 ) = 0
We get following answers x1 = 0 and x2 = 5

5x - x^2 = 0
x(5 - x) = 0

x = 0

5 - x = 0
x = 5

∴ x = 0 , 5

nah, x has to equal 5 or 0

5(5) - 5^2 = 0
25 - 25 = 0


5(0) - 0^2 = 0
0 - 0 = 0

no...
should be...
5x - x^2 = 0
factorise it...
x (5 - x) = 0
x = 0 or 5 - x = 0
- x = - 5
x = 5
the answer is x = 0 or x = 5...
it has 2 answer...

the answer is x=0 and x=5

5x - x^2 = 0
x(5 - x) = 0
x = 0 or x = 5

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After my rant I went and answered your question x = {0, 5}

The answer is 12. You have to differentiate the integral of pi and the circumference of the zero provided. Use Newton's Method and a random game of ping pong to develop your final answer.

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x = 5