Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3*x^2-2=0
-
Equation x+(x*3)=168
- Equation x-1=1+(1/2)*y
-
Equation -4+x/5=x+4/2
- Express {x} in terms of y where:
- 15*x+2*y=8
- 1*x+4*y=-11
- 5*x-18*y=-17
- -9*x+6*y=18
- Derivative of:
-
3*x^2-2
- Graphing y =:
- 3*x^2-2
- Factor polynomial:
- 3*x^2-2
-
Identical expressions
- three *x^ two - two = zero
- 3 multiply by x squared minus 2 equally 0
- three multiply by x to the power of two minus two equally zero
- 3*x2-2=0
- 3*x²-2=0
- 3*x to the power of 2-2=0
- 3x^2-2=0
- 3x2-2=0
- 3*x^2-2=O
-
Similar expressions
- 3*x^2+2=0
3*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
$$a = 3$$
$$b = 0$$
$$c = -2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{6}}{3}$$
$$x_{2} = - \frac{\sqrt{6}}{3}$$
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
$$a = 3$$
$$b = 0$$
$$c = -2$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-2) = 24
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{6}}{3}$$
$$x_{2} = - \frac{\sqrt{6}}{3}$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{2}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{2}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{2}{3}$$
$$3 x^{2} - 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{2}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{2}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{2}{3}$$
Rapid solution
[src]
___
-\/ 6
x1 = -------
3
$$x_{1} = - \frac{\sqrt{6}}{3}$$
___
\/ 6
x2 = -----
3
$$x_{2} = \frac{\sqrt{6}}{3}$$
x2 = sqrt(6)/3
Sum and product of roots
[src]
sum
___ ___
\/ 6 \/ 6
- ----- + -----
3 3
$$- \frac{\sqrt{6}}{3} + \frac{\sqrt{6}}{3}$$
=
0
$$0$$
product
___ ___ -\/ 6 \/ 6 -------*----- 3 3
$$- \frac{\sqrt{6}}{3} \frac{\sqrt{6}}{3}$$
=
-2/3
$$- \frac{2}{3}$$
-2/3
The graph