Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -20*(x-13)=-220
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Equation x-x/12=55/12
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Equation 3^x=81
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Equation 12-x^2=11
- Express {x} in terms of y where:
- 18*x+19*y=7
- 16*x-15*y=4
- 1*x+6*y=6
- 20*x+9*y=17
- Integral of d{x}:
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x^2+2x+3
-
Identical expressions
- x^ two +2x+ three = zero
- x squared plus 2x plus 3 equally 0
- x to the power of two plus 2x plus three equally zero
- x2+2x+3=0
- x²+2x+3=0
- x to the power of 2+2x+3=0
- x^2+2x+3=O
-
Similar expressions
- x^2-2x+3=0
- x^2+2x-3=0
x^2+2x+3=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
$$a = 1$$
$$b = 2$$
$$c = 3$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = -1 + \sqrt{2} i$$
$$x_{2} = -1 - \sqrt{2} i$$
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
$$a = 1$$
$$b = 2$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (3) = -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
$$x_{1} = -1 + \sqrt{2} i$$
$$x_{2} = -1 - \sqrt{2} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 3$$
Rapid solution
[src]
___ x1 = -1 - I*\/ 2
$$x_{1} = -1 - \sqrt{2} i$$
___ x2 = -1 + I*\/ 2
$$x_{2} = -1 + \sqrt{2} i$$
x2 = -1 + sqrt(2)*i
Sum and product of roots
[src]
sum
___ ___ -1 - I*\/ 2 + -1 + I*\/ 2
$$\left(-1 - \sqrt{2} i\right) + \left(-1 + \sqrt{2} i\right)$$
=
-2
$$-2$$
product
/ ___\ / ___\ \-1 - I*\/ 2 /*\-1 + I*\/ 2 /
$$\left(-1 - \sqrt{2} i\right) \left(-1 + \sqrt{2} i\right)$$
=
3
$$3$$
3
Numerical answer
[src]
x1 = -1.0 - 1.4142135623731*i
x2 = -1.0 + 1.4142135623731*i
x2 = -1.0 + 1.4142135623731*i
The graph