Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 0,4(x-3)-1,6=5(0,1x-0,5)
-
Equation x-243=x/2-51
-
Equation x^3-2*x^2+x+3=0
-
Equation 2*sin(x)-3*cos(x)=0
- Express {x} in terms of y where:
- 5*x-15*y=13
- 18*x-15*y=-7
- 14*x-4*y=14
- 13*x+12*y=7
- Factor polynomial:
- x^2-6*x+3
-
Identical expressions
- x^ two - six *x+ three = zero
- x squared minus 6 multiply by x plus 3 equally 0
- x to the power of two minus six multiply by x plus three equally zero
- x2-6*x+3=0
- x²-6*x+3=0
- x to the power of 2-6*x+3=0
- x^2-6x+3=0
- x2-6x+3=0
- x^2-6*x+3=O
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Similar expressions
- x^2+6*x+3=0
- x^2-6*x-3=0
x^2-6*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
$$a = 1$$
$$b = -6$$
$$c = 3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{6} + 3$$
$$x_{2} = 3 - \sqrt{6}$$
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
$$a = 1$$
$$b = -6$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (3) = 24
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{6} + 3$$
$$x_{2} = 3 - \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 3$$
Sum and product of roots
[src]
sum
___ ___ 3 - \/ 6 + 3 + \/ 6
$$\left(3 - \sqrt{6}\right) + \left(\sqrt{6} + 3\right)$$
=
6
$$6$$
product
/ ___\ / ___\ \3 - \/ 6 /*\3 + \/ 6 /
$$\left(3 - \sqrt{6}\right) \left(\sqrt{6} + 3\right)$$
=
3
$$3$$
3
Rapid solution
[src]
___ x1 = 3 - \/ 6
$$x_{1} = 3 - \sqrt{6}$$
___ x2 = 3 + \/ 6
$$x_{2} = \sqrt{6} + 3$$
x2 = sqrt(6) + 3
The graph