Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x=0
-
Equation -5*x=25
-
Equation 5*sin(x)+cos(x)=5
-
Equation 25*x^2=16
- Express {x} in terms of y where:
- -11*x-1*y=12
- 6*x+4*y=15
- 3*x+19*y=4
- 8*x-9*y=-1
- Graphing y =:
- -x^2+2*x-3
- Factor squared:
- -x^2+2*x-3
-
Identical expressions
- -x^ two + two *x- three = zero
- minus x squared plus 2 multiply by x minus 3 equally 0
- minus x to the power of two plus two multiply by x minus three equally zero
- -x2+2*x-3=0
- -x²+2*x-3=0
- -x to the power of 2+2*x-3=0
- -x^2+2x-3=0
- -x2+2x-3=0
- -x^2+2*x-3=O
-
Similar expressions
- -x^2+2*x+3=0
- -x^2-2*x-3=0
- x^2+2*x-3=0
-x^2+2*x-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
rewrite the equation
$$\left(- x^{2} + 2 x\right) - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x + 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 3$$
$$\left(- x^{2} + 2 x\right) - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x + 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 3$$
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
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
Numerical answer
[src]
x1 = 1.0 + 1.4142135623731*i
x2 = 1.0 - 1.4142135623731*i
x2 = 1.0 - 1.4142135623731*i
The graph