Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2*x^2+5*x-12=0
-
Equation x^2+2x-8=0
-
Equation 6x+2=-1
-
Equation e^x=1
- Express {x} in terms of y where:
- 7*x-2*y=18
- 18*x+19*y=7
- 8*x-13*y=-12
- -10*x+13*y=5
- Derivative of:
-
x^2+8
- Integral of d{x}:
-
x^2+8
- Factor polynomial:
- x^2+8
-
Identical expressions
- x^ two + eight = zero
- x squared plus 8 equally 0
- x to the power of two plus eight equally zero
- x2+8=0
- x²+8=0
- x to the power of 2+8=0
- x^2+8=O
-
Similar expressions
- x^2-8=0
x^2+8=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
$$a = 1$$
$$b = 0$$
$$c = 8$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 2 \sqrt{2} i$$
$$x_{2} = - 2 \sqrt{2} i$$
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
$$a = 1$$
$$b = 0$$
$$c = 8$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (8) = -32
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
$$x_{1} = 2 \sqrt{2} i$$
$$x_{2} = - 2 \sqrt{2} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 8$$
Sum and product of roots
[src]
sum
___ ___ - 2*I*\/ 2 + 2*I*\/ 2
$$- 2 \sqrt{2} i + 2 \sqrt{2} i$$
=
0
$$0$$
product
___ ___ -2*I*\/ 2 *2*I*\/ 2
$$- 2 \sqrt{2} i 2 \sqrt{2} i$$
=
8
$$8$$
8
Rapid solution
[src]
___ x1 = -2*I*\/ 2
$$x_{1} = - 2 \sqrt{2} i$$
___ x2 = 2*I*\/ 2
$$x_{2} = 2 \sqrt{2} i$$
x2 = 2*sqrt(2)*i
The graph