Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 7*x^3-28*x=0
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Equation sin(x)=0
- Equation z^2-(2-i)z+3-i=0
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Equation (5-x)^2-x(2,5+x)=0
- Express {x} in terms of y where:
- -20*x+19*y=-16
- -7*x-17*y=-18
- 19*x-17*y=-18
- 8*x+16*y=7
- Integral of d{x}:
- 2*x^2+1
- Derivative of:
-
2*x^2+1
- Factor polynomial:
- 2*x^2+1
-
Identical expressions
- two *x^ two + one
- 2 multiply by x squared plus 1
- two multiply by x to the power of two plus one
- 2*x2+1
- 2*x²+1
- 2*x to the power of 2+1
- 2x^2+1
- 2x2+1
-
Similar expressions
- 2*x^2-1
2*x^2+1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 0$$
$$c = 1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{\sqrt{2} i}{2}$$
$$x_{2} = - \frac{\sqrt{2} i}{2}$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (2) * (1) = -8
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{2} i}{2}$$
$$x_{2} = - \frac{\sqrt{2} i}{2}$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{2}$$
$$2 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{2}$$
Rapid solution
[src]
___
-I*\/ 2
x1 = ---------
2
$$x_{1} = - \frac{\sqrt{2} i}{2}$$
___
I*\/ 2
x2 = -------
2
$$x_{2} = \frac{\sqrt{2} i}{2}$$
x2 = sqrt(2)*i/2
Sum and product of roots
[src]
sum
___ ___
I*\/ 2 I*\/ 2
- ------- + -------
2 2
$$- \frac{\sqrt{2} i}{2} + \frac{\sqrt{2} i}{2}$$
=
0
$$0$$
product
___ ___
-I*\/ 2 I*\/ 2
---------*-------
2 2
$$- \frac{\sqrt{2} i}{2} \frac{\sqrt{2} i}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2