Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+3x+2=0
- Equation x+y=5
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Equation sin(x)=3
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Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
- Graphing y =:
- x^2-4*x+6
- Factor polynomial:
- x^2-4*x+6
-
Identical expressions
- x^ two - four *x+ six = zero
- x squared minus 4 multiply by x plus 6 equally 0
- x to the power of two minus four multiply by x plus six equally zero
- x2-4*x+6=0
- x²-4*x+6=0
- x to the power of 2-4*x+6=0
- x^2-4x+6=0
- x2-4x+6=0
- x^2-4*x+6=O
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Similar expressions
- x^2-4*x-6=0
- x^2+4*x+6=0
x^2-4*x+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
$$a = 1$$
$$b = -4$$
$$c = 6$$
, 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
$$a = 1$$
$$b = -4$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (6) = -8
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
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 6$$
Sum and product of roots
[src]
sum
___ ___ 2 - I*\/ 2 + 2 + I*\/ 2
$$\left(2 - \sqrt{2} i\right) + \left(2 + \sqrt{2} i\right)$$
=
4
$$4$$
product
/ ___\ / ___\ \2 - I*\/ 2 /*\2 + I*\/ 2 /
$$\left(2 - \sqrt{2} i\right) \left(2 + \sqrt{2} i\right)$$
=
6
$$6$$
6
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
Numerical answer
[src]
x1 = 2.0 - 1.4142135623731*i
x2 = 2.0 + 1.4142135623731*i
x2 = 2.0 + 1.4142135623731*i
The graph