Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1+sin(x)=0
-
Equation tg(x)=1
-
Equation x^4+4=0
-
Equation -x-4+5(x+3)=5(-1-x)-2
- Express {x} in terms of y where:
- 4*x+2*y=5
- 1*x+10*y=-18
- -18*x-2*y=9
- -11*x+9*y=-20
- Derivative of:
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x^2-2
- Integral of d{x}:
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x^2-2
- Graphing y =:
- x^2-2
-
Identical expressions
- x^ two - two = zero
- x squared minus 2 equally 0
- x to the power of two minus two equally zero
- x2-2=0
- x²-2=0
- x to the power of 2-2=0
- x^2-2=O
-
Similar expressions
- 1/3x^2-27=0
- 7x^2-21=0
- 3*(x^2-2*x-4)=-2*(x^2+3x+6)
- (x^2-2*x)/(x+3)=0
- x^2+2=0
- (x^2+x+2)/(x^2-2x+а^2+6а)=0
x^2-2=0 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
$$a = 1$$
$$b = 0$$
$$c = -2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{2}$$
$$x_{2} = - \sqrt{2}$$
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
$$a = 1$$
$$b = 0$$
$$c = -2$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-2) = 8
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{2}$$
$$x_{2} = - \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -2$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -2$$
Rapid solution
[src]
___ x1 = -\/ 2
$$x_{1} = - \sqrt{2}$$
___ x2 = \/ 2
$$x_{2} = \sqrt{2}$$
x2 = sqrt(2)
Sum and product of roots
[src]
sum
___ ___ - \/ 2 + \/ 2
$$- \sqrt{2} + \sqrt{2}$$
=
0
$$0$$
product
___ ___ -\/ 2 *\/ 2
$$- \sqrt{2} \sqrt{2}$$
=
-2
$$-2$$
-2
The graph