Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5^x=8^x
-
Equation -27x+220=-5x
-
Equation x+12=5
-
Equation 3/(x-5)+8/x=2
- Express {x} in terms of y where:
- 12*x+1*y=15
- -16*x-10*y=4
- -15*x-13*y=-20
- -4*x-20*y=10
-
Identical expressions
- three (x- two)(x+ four)= zero
- 3(x minus 2)(x plus 4) equally 0
- three (x minus two)(x plus four) equally zero
- 3x-2x+4=0
- 3(x-2)(x+4)=O
-
Similar expressions
- 3(x-2)(x-4)=0
- 6-3x-2(x+4,5)=x-27
- 3x-2x+4=8
- 3(x+2)(x+4)=0
- 6-3x-2(x+4.5)=x-27
3(x-2)(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
$$3 \left(x - 2\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$3 x^{2} + 6 x - 24 = 0$$
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
$$a = 3$$
$$b = 6$$
$$c = -24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -4$$
$$3 \left(x - 2\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$3 x^{2} + 6 x - 24 = 0$$
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
$$a = 3$$
$$b = 6$$
$$c = -24$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (3) * (-24) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -4$$
Sum and product of roots
[src]
sum
-4 + 2
$$-4 + 2$$
=
-2
$$-2$$
product
-4*2
$$- 8$$
=
-8
$$-8$$
-8