Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=cos(x)
-
Equation cos(x/2)=1/2
-
Equation sin(x)=√3/2
-
Equation sin(x)=1,5
- Express {x} in terms of y where:
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- sqrt(1-x)^2+(4-y)^2=0
- lnx+sin(y/x+2x)=4
-
Identical expressions
- x³-11x²-9x- ninety-nine = zero
- x³ minus 11x² minus 9x minus 99 equally 0
- x³ minus 11x² minus 9x minus ninety minus nine equally zero
- x³-11x²-9x-99=O
-
Similar expressions
- x³-11x²-9x+99=0
- x³+11x²-9x-99=0
- x³-11x²+9x-99=0
x³-11x²-9x-99=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3 2 x - 11*x - 9*x - 99 = 0
$$\left(- 9 x + \left(x^{3} - 11 x^{2}\right)\right) - 99 = 0$$
Vieta's Theorem
it is reduced cubic equation
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = -9$$
$$v = \frac{d}{a}$$
$$v = -99$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 11$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -9$$
$$x_{1} x_{2} x_{3} = -99$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = -9$$
$$v = \frac{d}{a}$$
$$v = -99$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 11$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -9$$
$$x_{1} x_{2} x_{3} = -99$$
Rapid solution
[src]
__________________ / __________________ \
/ _______ | / _______ |
/ 3113 \/ 79617 | ___ / 3113 \/ 79617 |
3 / ---- + --------- | \/ 3 *3 / ---- + --------- ___ |
11 74 \/ 27 3 | \/ 27 3 74*\/ 3 |
x1 = -- - ------------------------- - ----------------------- + I*|- ----------------------------- + -------------------------|
3 __________________ 2 | 2 __________________|
/ _______ | / _______ |
/ 3113 \/ 79617 | / 3113 \/ 79617 |
9*3 / ---- + --------- | 9*3 / ---- + --------- |
\/ 27 3 \ \/ 27 3 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} + \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}\right)$$
__________________ / __________________ \
/ _______ | / _______ |
/ 3113 \/ 79617 | ___ / 3113 \/ 79617 |
3 / ---- + --------- |\/ 3 *3 / ---- + --------- ___ |
11 74 \/ 27 3 | \/ 27 3 74*\/ 3 |
x2 = -- - ------------------------- - ----------------------- + I*|----------------------------- - -------------------------|
3 __________________ 2 | 2 __________________|
/ _______ | / _______ |
/ 3113 \/ 79617 | / 3113 \/ 79617 |
9*3 / ---- + --------- | 9*3 / ---- + --------- |
\/ 27 3 \ \/ 27 3 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2}\right)$$
__________________
/ _______
11 / 3113 \/ 79617 148
x3 = -- + 3 / ---- + --------- + -------------------------
3 \/ 27 3 __________________
/ _______
/ 3113 \/ 79617
9*3 / ---- + ---------
\/ 27 3
$$x_{3} = \frac{148}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}$$
x3 = 148/(9*(sqrt(79617)/3 + 3113/27)^(1/3)) + 11/3 + (sqrt(79617)/3 + 3113/27)^(1/3)
Sum and product of roots
[src]
sum
__________________ / __________________ \ __________________ / __________________ \
/ _______ | / _______ | / _______ | / _______ |
/ 3113 \/ 79617 | ___ / 3113 \/ 79617 | / 3113 \/ 79617 | ___ / 3113 \/ 79617 | __________________
3 / ---- + --------- | \/ 3 *3 / ---- + --------- ___ | 3 / ---- + --------- |\/ 3 *3 / ---- + --------- ___ | / _______
11 74 \/ 27 3 | \/ 27 3 74*\/ 3 | 11 74 \/ 27 3 | \/ 27 3 74*\/ 3 | 11 / 3113 \/ 79617 148
-- - ------------------------- - ----------------------- + I*|- ----------------------------- + -------------------------| + -- - ------------------------- - ----------------------- + I*|----------------------------- - -------------------------| + -- + 3 / ---- + --------- + -------------------------
3 __________________ 2 | 2 __________________| 3 __________________ 2 | 2 __________________| 3 \/ 27 3 __________________
/ _______ | / _______ | / _______ | / _______ | / _______
/ 3113 \/ 79617 | / 3113 \/ 79617 | / 3113 \/ 79617 | / 3113 \/ 79617 | / 3113 \/ 79617
9*3 / ---- + --------- | 9*3 / ---- + --------- | 9*3 / ---- + --------- | 9*3 / ---- + --------- | 9*3 / ---- + ---------
\/ 27 3 \ \/ 27 3 / \/ 27 3 \ \/ 27 3 / \/ 27 3
$$\left(\frac{148}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} + \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2}\right)\right)\right)$$
=
/ __________________ \ / __________________ \
| / _______ | | / _______ |
| ___ / 3113 \/ 79617 | | ___ / 3113 \/ 79617 |
|\/ 3 *3 / ---- + --------- ___ | | \/ 3 *3 / ---- + --------- ___ |
| \/ 27 3 74*\/ 3 | | \/ 27 3 74*\/ 3 |
11 + I*|----------------------------- - -------------------------| + I*|- ----------------------------- + -------------------------|
| 2 __________________| | 2 __________________|
| / _______ | | / _______ |
| / 3113 \/ 79617 | | / 3113 \/ 79617 |
| 9*3 / ---- + --------- | | 9*3 / ---- + --------- |
\ \/ 27 3 / \ \/ 27 3 /
$$11 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} + \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}\right) + i \left(- \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2}\right)$$
product
/ __________________ / __________________ \\ / __________________ / __________________ \\ | / _______ | / _______ || | / _______ | / _______ || | / 3113 \/ 79617 | ___ / 3113 \/ 79617 || | / 3113 \/ 79617 | ___ / 3113 \/ 79617 || / __________________ \ | 3 / ---- + --------- | \/ 3 *3 / ---- + --------- ___ || | 3 / ---- + --------- |\/ 3 *3 / ---- + --------- ___ || | / _______ | |11 74 \/ 27 3 | \/ 27 3 74*\/ 3 || |11 74 \/ 27 3 | \/ 27 3 74*\/ 3 || |11 / 3113 \/ 79617 148 | |-- - ------------------------- - ----------------------- + I*|- ----------------------------- + -------------------------||*|-- - ------------------------- - ----------------------- + I*|----------------------------- - -------------------------||*|-- + 3 / ---- + --------- + -------------------------| |3 __________________ 2 | 2 __________________|| |3 __________________ 2 | 2 __________________|| |3 \/ 27 3 __________________| | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 3113 \/ 79617 | / 3113 \/ 79617 || | / 3113 \/ 79617 | / 3113 \/ 79617 || | / 3113 \/ 79617 | | 9*3 / ---- + --------- | 9*3 / ---- + --------- || | 9*3 / ---- + --------- | 9*3 / ---- + --------- || | 9*3 / ---- + --------- | \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 \ \/ 27 3 // \ \/ 27 3 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} - \frac{74}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}{2} + \frac{74 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}}\right)\right) \left(\frac{148}{9 \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}} + \frac{11}{3} + \sqrt[3]{\frac{\sqrt{79617}}{3} + \frac{3113}{27}}\right)$$
=
99
$$99$$
99
Numerical answer
[src]
x1 = 12.3739145865352
x2 = -0.686957293267614 + 2.74386432248539*i
x3 = -0.686957293267614 - 2.74386432248539*i
x3 = -0.686957293267614 - 2.74386432248539*i