Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+4*x+4=0
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Equation (x^2-4)^2+(x^2-3x-10)^2=0
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Equation -x/3+x+7=3
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Equation -20*(x-13)=-220
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Identical expressions
- nine *x+x^ three + six *x^ two = zero
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- nine multiply by x plus x to the power of three plus six multiply by x to the power of two equally zero
- 9*x+x3+6*x2=0
- 9*x+x³+6*x²=0
- 9*x+x to the power of 3+6*x to the power of 2=0
- 9x+x^3+6x^2=0
- 9x+x3+6x2=0
- 9*x+x^3+6*x^2=O
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Similar expressions
- 9*x-x^3+6*x^2=0
- 9*x+x^3-6*x^2=0
9*x+x^3+6*x^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$6 x^{2} + \left(x^{3} + 9 x\right) = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} + 6 x + 9\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} + 6 x + 9 = 0$$
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
$$a = 1$$
$$b = 6$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{2} = -3$$
The final answer for 9*x + x^3 + 6*x^2 = 0:
$$x_{1} = 0$$
$$x_{2} = -3$$
$$6 x^{2} + \left(x^{3} + 9 x\right) = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(x^{2} + 6 x + 9\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$x^{2} + 6 x + 9 = 0$$
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
$$a = 1$$
$$b = 6$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -6/2/(1)
$$x_{2} = -3$$
The final answer for 9*x + x^3 + 6*x^2 = 0:
$$x_{1} = 0$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced cubic equation
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -6$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 9$$
$$v = \frac{d}{a}$$
$$v = 0$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -6$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9$$
$$x_{1} x_{2} x_{3} = 0$$
The graph