Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+2*x+10=0
-
Equation x^2+3*x+9=0
- Equation x^2-x+30=0
-
Equation 3*x^2-2*x-8=0
- Express {x} in terms of y where:
- -18*x-3*y=2
- 5*x+20*y=-4
- 20*x-8*y=13
- -16*x+18*y=9
- Graphing y =:
- x^2-6*x-3
- Factor polynomial:
- x^2-6*x-3
-
Identical expressions
- x^ two - six *x- three = zero
- x squared minus 6 multiply by x minus 3 equally 0
- x to the power of two minus six multiply by x minus 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
-
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
$$x_{1} = 3 + 2 \sqrt{3}$$
$$x_{2} = 3 - 2 \sqrt{3}$$
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) = 48
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3 + 2 \sqrt{3}$$
$$x_{2} = 3 - 2 \sqrt{3}$$
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 - 2*\/ 3 + 3 + 2*\/ 3
$$\left(3 - 2 \sqrt{3}\right) + \left(3 + 2 \sqrt{3}\right)$$
=
6
$$6$$
product
/ ___\ / ___\ \3 - 2*\/ 3 /*\3 + 2*\/ 3 /
$$\left(3 - 2 \sqrt{3}\right) \left(3 + 2 \sqrt{3}\right)$$
=
-3
$$-3$$
-3
Rapid solution
[src]
___ x1 = 3 - 2*\/ 3
$$x_{1} = 3 - 2 \sqrt{3}$$
___ x2 = 3 + 2*\/ 3
$$x_{2} = 3 + 2 \sqrt{3}$$
x2 = 3 + 2*sqrt(3)
The graph