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- Equation:
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Equation e^x=4
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Identical expressions
- x^ two - eight *x+ six = zero
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- x2-8*x+6=0
- x²-8*x+6=0
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- x2-8x+6=0
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Similar expressions
- x^2+8*x+6=0
- x^2-8*x-6=0
x^2-8*x+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
$$x_{1} = \sqrt{10} + 4$$
$$x_{2} = 4 - \sqrt{10}$$
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) = 40
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{10} + 4$$
$$x_{2} = 4 - \sqrt{10}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 6$$
Rapid solution
[src]
____ x1 = 4 - \/ 10
$$x_{1} = 4 - \sqrt{10}$$
____ x2 = 4 + \/ 10
$$x_{2} = \sqrt{10} + 4$$
x2 = sqrt(10) + 4
Sum and product of roots
[src]
sum
____ ____ 4 - \/ 10 + 4 + \/ 10
$$\left(4 - \sqrt{10}\right) + \left(\sqrt{10} + 4\right)$$
=
8
$$8$$
product
/ ____\ / ____\ \4 - \/ 10 /*\4 + \/ 10 /
$$\left(4 - \sqrt{10}\right) \left(\sqrt{10} + 4\right)$$
=
6
$$6$$
6
The graph