Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=5
-
Equation 2x=4
-
Equation x^2=x+72
-
Equation 7/(x-5)=2
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
-
Identical expressions
- x^ two - four |x|+8x= zero
- x squared minus 4 module of x| plus 8x equally 0
- x to the power of two minus four module of x| plus 8x equally zero
- x2-4|x|+8x=0
- x²-4|x|+8x=0
- x to the power of 2-4|x|+8x=0
- x^2-4|x|+8x=O
-
Similar expressions
- x^2+4|x|+8x=0
- x^2-4|x|-8x=0
x^2-4|x|+8x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x^{2} - 4 x + 8 x = 0$$
after simplifying we get
$$x^{2} + 4 x = 0$$
the solution in this interval:
$$x_{1} = -4$$
but x1 not in the inequality interval
$$x_{2} = 0$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$x^{2} - 4 \left(- x\right) + 8 x = 0$$
after simplifying we get
$$x^{2} + 12 x = 0$$
the solution in this interval:
$$x_{3} = -12$$
$$x_{4} = 0$$
but x4 not in the inequality interval
The final answer:
$$x_{1} = 0$$
$$x_{2} = -12$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x^{2} - 4 x + 8 x = 0$$
after simplifying we get
$$x^{2} + 4 x = 0$$
the solution in this interval:
$$x_{1} = -4$$
but x1 not in the inequality interval
$$x_{2} = 0$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$x^{2} - 4 \left(- x\right) + 8 x = 0$$
after simplifying we get
$$x^{2} + 12 x = 0$$
the solution in this interval:
$$x_{3} = -12$$
$$x_{4} = 0$$
but x4 not in the inequality interval
The final answer:
$$x_{1} = 0$$
$$x_{2} = -12$$
Sum and product of roots
[src]
sum
0 - 12 + 0
$$\left(-12 + 0\right) + 0$$
=
-12
$$-12$$
product
1*-12*0
$$1 \left(-12\right) 0$$
=
0
$$0$$
0
The graph