Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*sin(x)=0
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Equation (x-5)^2-x^2=3
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Equation -2*(-y-2)-y-2=0
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Equation x^2+x=6
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Identical expressions
- (4x- twelve)*(x+ six)= zero
- (4x minus 12) multiply by (x plus 6) equally 0
- (4x minus twelve) multiply by (x plus six) equally zero
- (4x-12)(x+6)=0
- 4x-12x+6=0
- (4x-12)*(x+6)=O
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Similar expressions
- (4x+12)*(x+6)=0
- (4x-12)*(x-6)=0
(4x-12)*(x+6)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 6\right) \left(4 x - 12\right) = 0$$
We get the quadratic equation
$$4 x^{2} + 12 x - 72 = 0$$
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
$$a = 4$$
$$b = 12$$
$$c = -72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = -6$$
$$\left(x + 6\right) \left(4 x - 12\right) = 0$$
We get the quadratic equation
$$4 x^{2} + 12 x - 72 = 0$$
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
$$a = 4$$
$$b = 12$$
$$c = -72$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (4) * (-72) = 1296
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = -6$$
Sum and product of roots
[src]
sum
-6 + 3
$$-6 + 3$$
=
-3
$$-3$$
product
-6*3
$$- 18$$
=
-18
$$-18$$
-18