Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=1/5
-
Equation x^2+11=0
-
Equation x^2+5x+6=0
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Equation -x/7+x=15/7
- Express {x} in terms of y where:
- 9*x+17*y=13
- 20*x+18*y=-9
- -4*x-8*y=-20
- -1*x+4*y=-10
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Identical expressions
- x^ four + ten *x+ nine = zero
- x to the power of 4 plus 10 multiply by x plus 9 equally 0
- x to the power of four plus ten multiply by x plus nine equally zero
- x4+10*x+9=0
- x⁴+10*x+9=0
- x^4+10x+9=0
- x4+10x+9=0
- x^4+10*x+9=O
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Similar expressions
- x^4-10*x+9=0
- x^4+10*x-9=0
x^4+10*x+9=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
x1 = -1
$$x_{1} = -1$$
_________________ / _________________\
3 / _____ | ___ ___ 3 / _____ |
1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 |
x2 = - - ---------------------- + -------------------- + I*|---------------------- + --------------------------|
3 _________________ 6 | _________________ 6 |
3 / _____ | 3 / _____ |
3*\/ 125 + 9*\/ 193 \3*\/ 125 + 9*\/ 193 /
$$x_{2} = - \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6}\right)$$
_________________ / _________________\
3 / _____ | ___ ___ 3 / _____ |
1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 |
x3 = - - ---------------------- + -------------------- + I*|- ---------------------- - --------------------------|
3 _________________ 6 | _________________ 6 |
3 / _____ | 3 / _____ |
3*\/ 125 + 9*\/ 193 \ 3*\/ 125 + 9*\/ 193 /
$$x_{3} = - \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6} - \frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}}\right)$$
_________________
3 / _____
1 \/ 125 + 9*\/ 193 2
x4 = - - -------------------- + ----------------------
3 3 _________________
3 / _____
3*\/ 125 + 9*\/ 193
$$x_{4} = - \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{3} + \frac{2}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3}$$
x4 = -(125 + 9*sqrt(193))^(1/3)/3 + 2/(3*(125 + 9*sqrt(193))^(1/3)) + 1/3
Sum and product of roots
[src]
sum
_________________ / _________________\ _________________ / _________________\ _________________
3 / _____ | ___ ___ 3 / _____ | 3 / _____ | ___ ___ 3 / _____ | 3 / _____
1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 | 1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 | 1 \/ 125 + 9*\/ 193 2
-1 + - - ---------------------- + -------------------- + I*|---------------------- + --------------------------| + - - ---------------------- + -------------------- + I*|- ---------------------- - --------------------------| + - - -------------------- + ----------------------
3 _________________ 6 | _________________ 6 | 3 _________________ 6 | _________________ 6 | 3 3 _________________
3 / _____ | 3 / _____ | 3 / _____ | 3 / _____ | 3 / _____
3*\/ 125 + 9*\/ 193 \3*\/ 125 + 9*\/ 193 / 3*\/ 125 + 9*\/ 193 \ 3*\/ 125 + 9*\/ 193 / 3*\/ 125 + 9*\/ 193
$$\left(- \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{3} + \frac{2}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3}\right) + \left(\left(- \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6} - \frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}}\right)\right) + \left(-1 + \left(- \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6}\right)\right)\right)\right)$$
=
/ _________________\ / _________________\ | ___ ___ 3 / _____ | | ___ ___ 3 / _____ | | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 | | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 | I*|- ---------------------- - --------------------------| + I*|---------------------- + --------------------------| | _________________ 6 | | _________________ 6 | | 3 / _____ | | 3 / _____ | \ 3*\/ 125 + 9*\/ 193 / \3*\/ 125 + 9*\/ 193 /
$$i \left(- \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6} - \frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}}\right) + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6}\right)$$
product
/ _________________ / _________________\\ / _________________ / _________________\\ / _________________ \ | 3 / _____ | ___ ___ 3 / _____ || | 3 / _____ | ___ ___ 3 / _____ || | 3 / _____ | |1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 || |1 1 \/ 125 + 9*\/ 193 | \/ 3 \/ 3 *\/ 125 + 9*\/ 193 || |1 \/ 125 + 9*\/ 193 2 | -|- - ---------------------- + -------------------- + I*|---------------------- + --------------------------||*|- - ---------------------- + -------------------- + I*|- ---------------------- - --------------------------||*|- - -------------------- + ----------------------| |3 _________________ 6 | _________________ 6 || |3 _________________ 6 | _________________ 6 || |3 3 _________________| | 3 / _____ | 3 / _____ || | 3 / _____ | 3 / _____ || | 3 / _____ | \ 3*\/ 125 + 9*\/ 193 \3*\/ 125 + 9*\/ 193 // \ 3*\/ 125 + 9*\/ 193 \ 3*\/ 125 + 9*\/ 193 // \ 3*\/ 125 + 9*\/ 193 /
$$- (- \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6}\right)) \left(- \frac{1}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3} + \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{125 + 9 \sqrt{193}}}{6} - \frac{\sqrt{3}}{3 \sqrt[3]{125 + 9 \sqrt{193}}}\right)\right) \left(- \frac{\sqrt[3]{125 + 9 \sqrt{193}}}{3} + \frac{2}{3 \sqrt[3]{125 + 9 \sqrt{193}}} + \frac{1}{3}\right)$$
=
9
$$9$$
9
Numerical answer
[src]
x1 = 1.33040121988528 + 1.9102617040202*i
x2 = 1.33040121988528 - 1.9102617040202*i
x3 = -1.66080243977055
x4 = -1.0
x4 = -1.0