Mister Exam
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How to use it?
- Equation:
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Equation -x=5
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Equation x/3+x/12=15/4
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Identical expressions
- -x^ two +8x+ six = zero
- minus x squared plus 8x plus 6 equally 0
- minus x to the power of two plus 8x plus six equally zero
- -x2+8x+6=0
- -x²+8x+6=0
- -x to the power of 2+8x+6=0
- -x^2+8x+6=O
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Similar expressions
- -x^2-8x+6=0
- -x^2+8x-6=0
- x^2+8x+6=0
-x^2+8x+6=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
$$a = -1$$
$$b = 8$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4 - \sqrt{22}$$
Simplify
$$x_{2} = 4 + \sqrt{22}$$
Simplify
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
$$a = -1$$
$$b = 8$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (-1) * (6) = 88
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4 - \sqrt{22}$$
Simplify
$$x_{2} = 4 + \sqrt{22}$$
Simplify
Vieta's Theorem
rewrite the equation
$$- x^{2} + 8 x + 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 8 x - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -6$$
$$- x^{2} + 8 x + 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 8 x - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -6$$
Sum and product of roots
[src]
sum
____ ____ 0 + 4 - \/ 22 + 4 + \/ 22
$$\left(\left(4 - \sqrt{22}\right) + 0\right) + \left(4 + \sqrt{22}\right)$$
=
8
$$8$$
product
/ ____\ / ____\ 1*\4 - \/ 22 /*\4 + \/ 22 /
$$1 \cdot \left(4 - \sqrt{22}\right) \left(4 + \sqrt{22}\right)$$
=
-6
$$-6$$
-6
Rapid solution
[src]
____ x1 = 4 - \/ 22
$$x_{1} = 4 - \sqrt{22}$$
____ x2 = 4 + \/ 22
$$x_{2} = 4 + \sqrt{22}$$
The graph