Mister Exam
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How to use it?
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Equation 5-x=4(x-3)
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Equation -(-y+4)+2*y+1=0
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- -16*x-20*y=-13
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Identical expressions
- -x^ three +(one thousand, four hundred and sixty-nine / one thousand)*x^ two - zero . one thousand, eight hundred and forty-one *x+(three / five hundred)= zero
- minus x cubed plus (1469 divide by 1000) multiply by x squared minus 0.1841 multiply by x plus (3 divide by 500) equally 0
- minus x to the power of three plus (one thousand, four hundred and sixty minus nine divide by one thousand) multiply by x to the power of two minus zero . one thousand, eight hundred and forty minus one multiply by x plus (three divide by five hundred) equally zero
- -x3+(1469/1000)*x2-0.1841*x+(3/500)=0
- -x3+1469/1000*x2-0.1841*x+3/500=0
- -x³+(1469/1000)*x²-0.1841*x+(3/500)=0
- -x to the power of 3+(1469/1000)*x to the power of 2-0.1841*x+(3/500)=0
- -x^3+(1469/1000)x^2-0.1841x+(3/500)=0
- -x3+(1469/1000)x2-0.1841x+(3/500)=0
- -x3+1469/1000x2-0.1841x+3/500=0
- -x^3+1469/1000x^2-0.1841x+3/500=0
- -x^3+(1469/1000)*x^2-0.1841*x+(3/500)=O
- -x^3+(1469 divide by 1000)*x^2-0.1841*x+(3 divide by 500)=0
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Similar expressions
- x^3+(1469/1000)*x^2-0.1841*x+(3/500)=0
- -x^3-(1469/1000)*x^2-0.1841*x+(3/500)=0
- -x^3+(1469/1000)*x^2+0.1841*x+(3/500)=0
- -x^3+(1469/1000)*x^2-0.1841*x-(3/500)=0
-x^3+(1469/1000)*x^2-0.1841*x+(3/500)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2
3 1469*x 3
- x + ------- - 0.1841*x + --- = 0
1000 500
$$\left(- 0.1841 x + \left(- x^{3} + \frac{1469 x^{2}}{1000}\right)\right) + \frac{3}{500} = 0$$
Vieta's Theorem
rewrite the equation
$$\left(- 0.1841 x + \left(- x^{3} + \frac{1469 x^{2}}{1000}\right)\right) + \frac{3}{500} = 0$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{1469 x^{2}}{1000} + 0.1841 x - \frac{3}{500} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1469}{1000}$$
$$q = \frac{c}{a}$$
$$q = 0.1841$$
$$v = \frac{d}{a}$$
$$v = - \frac{3}{500}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{1469}{1000}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0.1841$$
$$x_{1} x_{2} x_{3} = - \frac{3}{500}$$
$$\left(- 0.1841 x + \left(- x^{3} + \frac{1469 x^{2}}{1000}\right)\right) + \frac{3}{500} = 0$$
of
$$a x^{3} + b x^{2} + c x + d = 0$$
as reduced cubic equation
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - \frac{1469 x^{2}}{1000} + 0.1841 x - \frac{3}{500} = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1469}{1000}$$
$$q = \frac{c}{a}$$
$$q = 0.1841$$
$$v = \frac{d}{a}$$
$$v = - \frac{3}{500}$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = \frac{1469}{1000}$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0.1841$$
$$x_{1} x_{2} x_{3} = - \frac{3}{500}$$
Rapid solution
[src]
x1 = 0.0615933668694125 + 0.e-23*I
$$x_{1} = 0.0615933668694125 + 3.0 \cdot 10^{-23} i$$
x2 = 0.0730011120076667 - 0.e-23*I
$$x_{2} = 0.0730011120076667 - 1.0 \cdot 10^{-23} i$$
x3 = 1.33440552112292 - 0.e-23*I
$$x_{3} = 1.33440552112292 - 1.0 \cdot 10^{-23} i$$
x3 = 1.33440552112292 - 0.e-23*i
Sum and product of roots
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sum
0.0615933668694125 + 0.e-23*I + 0.0730011120076667 - 0.e-23*I + 1.33440552112292 - 0.e-23*I
$$\left(1.33440552112292 - 1.0 \cdot 10^{-23} i\right) + \left(\left(0.0730011120076667 - 1.0 \cdot 10^{-23} i\right) + \left(0.0615933668694125 + 3.0 \cdot 10^{-23} i\right)\right)$$
=
1.46900000000000
$$1.469$$
product
(0.0615933668694125 + 0.e-23*I)*(0.0730011120076667 - 0.e-23*I)*(1.33440552112292 - 0.e-23*I)
$$\left(0.0615933668694125 + 3.0 \cdot 10^{-23} i\right) \left(0.0730011120076667 - 1.0 \cdot 10^{-23} i\right) \left(1.33440552112292 - 1.0 \cdot 10^{-23} i\right)$$
=
0.006 + 1.43121119895216e-24*I
$$0.006 + 1.43121119895216 \cdot 10^{-24} i$$
0.006 + 1.43121119895216e-24*i
Numerical answer
[src]
x1 = 0.0730011120076667
x2 = 1.33440552112292
x3 = 0.0615933668694125
x3 = 0.0615933668694125