Mister Exam
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Identical expressions
- one /3x^ two - twenty-seven = zero
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Similar expressions
- 1/3x^2+27=0
1/3x^2-27=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(\frac{x^{2}}{3} - 27\right) + 0 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{3} - 27 = 0$$
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
$$a = \frac{1}{3}$$
$$b = 0$$
$$c = -27$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
Simplify
$$x_{2} = -9$$
Simplify
$$\left(\frac{x^{2}}{3} - 27\right) + 0 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{3} - 27 = 0$$
This equation is of the form
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
$$a = \frac{1}{3}$$
$$b = 0$$
$$c = -27$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1/3) * (-27) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
Simplify
$$x_{2} = -9$$
Simplify
Vieta's Theorem
rewrite the equation
$$\frac{x^{2}}{3} - 27 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 81 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -81$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -81$$
$$\frac{x^{2}}{3} - 27 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 81 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -81$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -81$$
Sum and product of roots
[src]
sum
0 - 9 + 9
$$\left(-9 + 0\right) + 9$$
=
0
$$0$$
product
1*-9*9
$$1 \left(-9\right) 9$$
=
-81
$$-81$$
-81
The graph