Mister Exam
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Identical expressions
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Similar expressions
- (3x−36)⋅(x-8)=0
(3x−36)⋅(x+8)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 8\right) \left(3 x - 36\right) = 0$$
We get the quadratic equation
$$3 x^{2} - 12 x - 288 = 0$$
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
$$a = 3$$
$$b = -12$$
$$c = -288$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 12$$
$$x_{2} = -8$$
$$\left(x + 8\right) \left(3 x - 36\right) = 0$$
We get the quadratic equation
$$3 x^{2} - 12 x - 288 = 0$$
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
$$a = 3$$
$$b = -12$$
$$c = -288$$
, then
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (3) * (-288) = 3600
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 12$$
$$x_{2} = -8$$
Sum and product of roots
[src]
sum
-8 + 12
$$-8 + 12$$
=
4
$$4$$
product
-8*12
$$- 96$$
=
-96
$$-96$$
-96