Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x+7*4=40
-
Equation 6x^2+x-7=0
-
Equation 68+x*6=164
-
Equation 3*x^2+1=0
- Express {x} in terms of y where:
- 10*x+13*y=-12
- 14*x+7*y=19
- -3*x-9*y=7
- -6*x+13*y=-4
- Derivative of:
-
3*x^2+1
-
Identical expressions
- three *x^ two + one = zero
- 3 multiply by x squared plus 1 equally 0
- three multiply by x to the power of two plus one equally zero
- 3*x2+1=0
- 3*x²+1=0
- 3*x to the power of 2+1=0
- 3x^2+1=0
- 3x2+1=0
- 3*x^2+1=O
-
Similar expressions
- 3*x^2-1=0
3*x^2+1=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
$$a = 3$$
$$b = 0$$
$$c = 1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{\sqrt{3} i}{3}$$
$$x_{2} = - \frac{\sqrt{3} i}{3}$$
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
$$a = 3$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (1) = -12
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
$$x_{1} = \frac{\sqrt{3} i}{3}$$
$$x_{2} = - \frac{\sqrt{3} i}{3}$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{3}$$
$$3 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{3}$$
Rapid solution
[src]
___
-I*\/ 3
x1 = ---------
3
$$x_{1} = - \frac{\sqrt{3} i}{3}$$
___
I*\/ 3
x2 = -------
3
$$x_{2} = \frac{\sqrt{3} i}{3}$$
x2 = sqrt(3)*i/3
Sum and product of roots
[src]
sum
___ ___
I*\/ 3 I*\/ 3
- ------- + -------
3 3
$$- \frac{\sqrt{3} i}{3} + \frac{\sqrt{3} i}{3}$$
=
0
$$0$$
product
___ ___
-I*\/ 3 I*\/ 3
---------*-------
3 3
$$- \frac{\sqrt{3} i}{3} \frac{\sqrt{3} i}{3}$$
=
1/3
$$\frac{1}{3}$$
1/3
The graph