Mister Exam
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How to use it?
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Equation -60*x=-8
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Equation 2x+9=13-x
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- Express {x} in terms of y where:
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- Graphing y =:
- x^2-6x-11
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Identical expressions
- x^ two -6x- eleven = zero
- x squared minus 6x minus 11 equally 0
- x to the power of two minus 6x minus eleven equally zero
- x2-6x-11=0
- x²-6x-11=0
- x to the power of 2-6x-11=0
- x^2-6x-11=O
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Similar expressions
- x^2-6x+11=0
- x^2+6x-11=0
x^2-6x-11=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
$$a = 1$$
$$b = -6$$
$$c = -11$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3 + 2 \sqrt{5}$$
$$x_{2} = 3 - 2 \sqrt{5}$$
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
$$a = 1$$
$$b = -6$$
$$c = -11$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (-11) = 80
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3 + 2 \sqrt{5}$$
$$x_{2} = 3 - 2 \sqrt{5}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -11$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -11$$
Rapid solution
[src]
___ x1 = 3 - 2*\/ 5
$$x_{1} = 3 - 2 \sqrt{5}$$
___ x2 = 3 + 2*\/ 5
$$x_{2} = 3 + 2 \sqrt{5}$$
x2 = 3 + 2*sqrt(5)
Sum and product of roots
[src]
sum
___ ___ 3 - 2*\/ 5 + 3 + 2*\/ 5
$$\left(3 - 2 \sqrt{5}\right) + \left(3 + 2 \sqrt{5}\right)$$
=
6
$$6$$
product
/ ___\ / ___\ \3 - 2*\/ 5 /*\3 + 2*\/ 5 /
$$\left(3 - 2 \sqrt{5}\right) \left(3 + 2 \sqrt{5}\right)$$
=
-11
$$-11$$
-11
The graph