Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (5x-8)(4x-3)=0
- Equation x^2-4i=0
- Equation x^4-29x^2+100=0
- Equation tg^3x-tg^2x-3tgx+3=0
- Express {x} in terms of y where:
- 9*x-8*y=6
- 15*x+15*y=16
- -4*x+18*y=-14
- 8*x+7*y=-13
-
Identical expressions
- x^ two -4i= zero
- x squared minus 4i equally 0
- x to the power of two minus 4i equally zero
- x2-4i=0
- x²-4i=0
- x to the power of 2-4i=0
- x^2-4i=O
-
Similar expressions
- x^2+4i=0
x^2-4i=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
$$a = 1$$
$$b = 0$$
$$c = - 4 i$$
, then
The equation has two roots.
or
$$x_{1} = 2 \sqrt{i}$$
Simplify
$$x_{2} = - 2 \sqrt{i}$$
Simplify
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
$$a = 1$$
$$b = 0$$
$$c = - 4 i$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-4*i) = 16*i
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{i}$$
Simplify
$$x_{2} = - 2 \sqrt{i}$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \left(-1\right) 4 i$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \left(-1\right) 4 i$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \left(-1\right) 4 i$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \left(-1\right) 4 i$$
The graph
Rapid solution
[src]
___ ___ x1 = - \/ 2 - I*\/ 2
$$x_{1} = - \sqrt{2} - \sqrt{2} i$$
___ ___ x2 = \/ 2 + I*\/ 2
$$x_{2} = \sqrt{2} + \sqrt{2} i$$
Sum and product of roots
[src]
sum
___ ___ ___ ___ 0 + - \/ 2 - I*\/ 2 + \/ 2 + I*\/ 2
$$\left(0 - \left(\sqrt{2} + \sqrt{2} i\right)\right) + \left(\sqrt{2} + \sqrt{2} i\right)$$
=
0
$$0$$
product
/ ___ ___\ / ___ ___\ 1*\- \/ 2 - I*\/ 2 /*\\/ 2 + I*\/ 2 /
$$1 \left(- \sqrt{2} - \sqrt{2} i\right) \left(\sqrt{2} + \sqrt{2} i\right)$$
=
-4*I
$$- 4 i$$
-4*i
Numerical answer
[src]
x1 = -1.4142135623731 - 1.4142135623731*i
x2 = 1.4142135623731 + 1.4142135623731*i
x2 = 1.4142135623731 + 1.4142135623731*i