Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 10/(x+6)=1
-
Equation x^6=-64
-
Equation sin(5*x)=-1
-
Equation 5(x-7)=-3
- Express {x} in terms of y where:
- -5*x-13*y=-2
- -6*x-14*y=17
- -11*x-3*y=-1
- 16*x+7*y=-9
-
Identical expressions
- (3x- six)(4x- one , six)= zero
- (3x minus 6)(4x minus 1,6) equally 0
- (3x minus six)(4x minus one , six) equally zero
- 3x-64x-1,6=0
- (3x-6)(4x-1,6)=O
-
Similar expressions
- (3x-6)(4x+1,6)=0
- (3x+6)(4x-1,6)=0
(3x-6)(4x-1,6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(3*x - 6)*(4*x - 8/5) = 0
$$\left(3 x - 6\right) \left(4 x - \frac{8}{5}\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(3 x - 6\right) \left(4 x - \frac{8}{5}\right) = 0$$
We get the quadratic equation
$$12 x^{2} - \frac{144 x}{5} + \frac{48}{5} = 0$$
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
$$a = 12$$
$$b = - \frac{144}{5}$$
$$c = \frac{48}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = \frac{2}{5}$$
$$\left(3 x - 6\right) \left(4 x - \frac{8}{5}\right) = 0$$
We get the quadratic equation
$$12 x^{2} - \frac{144 x}{5} + \frac{48}{5} = 0$$
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
$$a = 12$$
$$b = - \frac{144}{5}$$
$$c = \frac{48}{5}$$
, then
D = b^2 - 4 * a * c =
(-144/5)^2 - 4 * (12) * (48/5) = 9216/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = \frac{2}{5}$$
Sum and product of roots
[src]
sum
2 + 2/5
$$\frac{2}{5} + 2$$
=
12/5
$$\frac{12}{5}$$
product
2*2 --- 5
$$\frac{2 \cdot 2}{5}$$
=
4/5
$$\frac{4}{5}$$
4/5