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-6)(4x-6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 6\right) \left(4 x - 6\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 30 x + 36 = 0$$
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
$$a = 4$$
$$b = -30$$
$$c = 36$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{2}$$
$$\left(x - 6\right) \left(4 x - 6\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 30 x + 36 = 0$$
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
$$a = 4$$
$$b = -30$$
$$c = 36$$
, then
D = b^2 - 4 * a * c =
(-30)^2 - 4 * (4) * (36) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
6 + 3/2
$$\frac{3}{2} + 6$$
=
15/2
$$\frac{15}{2}$$
product
6*3 --- 2
$$\frac{3 \cdot 6}{2}$$
=
9
$$9$$
9
The graph