Mister Exam
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How to use it?
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Identical expressions
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Similar expressions
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(x-3)*(x-4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 4\right) \left(x - 3\right) = 0$$
We get the quadratic equation
$$x^{2} - 7 x + 12 = 0$$
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
$$a = 1$$
$$b = -7$$
$$c = 12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = 3$$
$$\left(x - 4\right) \left(x - 3\right) = 0$$
We get the quadratic equation
$$x^{2} - 7 x + 12 = 0$$
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
$$a = 1$$
$$b = -7$$
$$c = 12$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (1) * (12) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = 3$$
Sum and product of roots
[src]
sum
3 + 4
$$3 + 4$$
=
7
$$7$$
product
3*4
$$3 \cdot 4$$
=
12
$$12$$
12
The graph