Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x^2-8=0
-
Equation x^2-3x+5=0
-
Equation x^2+10*x+24=0
-
Equation (x-8)^2=(x-2)^2
- Express {x} in terms of y where:
- 15*x-19*y=7
- -7*x-3*y=-9
- -11*x-3*y=-13
- -2*x-10*y=-17
- Integral of d{x}:
-
3x^2-1
- Graphing y =:
- 3x^2-1
- Derivative of:
-
3x^2-1
-
Identical expressions
- 3x^ two - one = zero
- 3x squared minus 1 equally 0
- 3x to the power of two minus one equally zero
- 3x2-1=0
- 3x²-1=0
- 3x to the power of 2-1=0
- 3x^2-1=O
-
Similar expressions
- 3x^2+1=0
3x^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 two roots.
or
$$x_{1} = \frac{\sqrt{3}}{3}$$
$$x_{2} = - \frac{\sqrt{3}}{3}$$
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 two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{3}}{3}$$
$$x_{2} = - \frac{\sqrt{3}}{3}$$
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]
___
-\/ 3
x1 = -------
3
$$x_{1} = - \frac{\sqrt{3}}{3}$$
___
\/ 3
x2 = -----
3
$$x_{2} = \frac{\sqrt{3}}{3}$$
x2 = sqrt(3)/3
Sum and product of roots
[src]
sum
___ ___
\/ 3 \/ 3
- ----- + -----
3 3
$$- \frac{\sqrt{3}}{3} + \frac{\sqrt{3}}{3}$$
=
0
$$0$$
product
___ ___ -\/ 3 \/ 3 -------*----- 3 3
$$- \frac{\sqrt{3}}{3} \frac{\sqrt{3}}{3}$$
=
-1/3
$$- \frac{1}{3}$$
-1/3
The graph