Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5*x^2=35*x
-
Equation 4*(x-8)=-5
-
Equation 4=7-6(5x-1)
-
Equation 50*x+60=210
- Express {x} in terms of y where:
- 8*x-16*y=14
- -17*x-8*y=7
- -3*x-20*y=-13
- 15*x-3*y=19
- Graphing y =:
- x^2+4*x+6
- Integral of d{x}:
- x^2+4*x+6
-
Identical expressions
- x^ two + four *x+ six = zero
- x squared plus 4 multiply by x plus 6 equally 0
- x to the power of two plus 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
-
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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 6$$
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
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
Numerical answer
[src]
x1 = -2.0 - 1.4142135623731*i
x2 = -2.0 + 1.4142135623731*i
x2 = -2.0 + 1.4142135623731*i
The graph