Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x^2-1)/(x+2)=4x
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation cos(x)=3/4
-
Equation 7+x=4
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 18*x-12*y=-20
- -13*x+7*y=11
- -19*x-14*y=-8
- Graphing y =:
- x^3-3*x^2
- Integral of d{x}:
-
x^3-3*x^2
- Derivative of:
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x^3-3*x^2
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Identical expressions
- x^ three - three *x^ two = zero
- x cubed minus 3 multiply by x squared equally 0
- x to the power of three minus three multiply by x to the power of two equally zero
- x3-3*x2=0
- x³-3*x²=0
- x to the power of 3-3*x to the power of 2=0
- x^3-3x^2=0
- x3-3x2=0
- x^3-3*x^2=O
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Similar expressions
- -2*x^3-3*x^2+18=0
- x^3+3*x^2=0
- x^3-3x^2+5
x^3-3*x^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$x^{3} - 3 x^{2} = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} - 3 x\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} - 3 x = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -3$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{2} = 3$$
$$x_{3} = 0$$
The final answer for x^3 - 3*x^2 = 0:
$$x_{1} = 0$$
$$x_{2} = 3$$
$$x_{3} = 0$$
$$x^{3} - 3 x^{2} = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} - 3 x\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} - 3 x = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -3$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (1) * (0) = 9
Because D > 0, then the equation has two roots.
x2 = (-b + sqrt(D)) / (2*a)
x3 = (-b - sqrt(D)) / (2*a)
or
$$x_{2} = 3$$
$$x_{3} = 0$$
The final answer for x^3 - 3*x^2 = 0:
$$x_{1} = 0$$
$$x_{2} = 3$$
$$x_{3} = 0$$
Vieta's Theorem
it is reduced cubic equation
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 0$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 3$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0$$
$$x_{1} x_{2} x_{3} = 0$$
The graph