Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -7x=4
-
Equation x^2-6=0
- Equation x^2-x-90=0
-
Equation -9x=36
- Express {x} in terms of y where:
- -6*x-11*y=-20
- -15*x+7*y=1
- -10*x+4*y=3
- -8*x-16*y=-1
- Integral of d{x}:
-
x^2-6
- Graphing y =:
- x^2-6
- Factor polynomial:
- x^2-6
-
Identical expressions
- x^ two - six = zero
- x squared minus 6 equally 0
- x to the power of two minus six equally zero
- x2-6=0
- x²-6=0
- x to the power of 2-6=0
- x^2-6=O
-
Similar expressions
- (x^2-36)/(x^2-6)=0
- x^2+6=0
x^2-6=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
$$a = 1$$
$$b = 0$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$
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
$$a = 1$$
$$b = 0$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-6) = 24
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
Sum and product of roots
[src]
sum
___ ___ - \/ 6 + \/ 6
$$- \sqrt{6} + \sqrt{6}$$
=
0
$$0$$
product
___ ___ -\/ 6 *\/ 6
$$- \sqrt{6} \sqrt{6}$$
=
-6
$$-6$$
-6
Rapid solution
[src]
___ x1 = -\/ 6
$$x_{1} = - \sqrt{6}$$
___ x2 = \/ 6
$$x_{2} = \sqrt{6}$$
x2 = sqrt(6)
The graph