Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=4
-
Equation x^2-x=12
-
Equation 9^x-8*3^x-9=0
-
Equation (|x+4|)=5
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -7*x-13*y=-12
- -10*x-12*y=-10
- 8*x+1*y=4
-
Identical expressions
- (x+ four)(3x- twelve)= zero
- (x plus 4)(3x minus 12) equally 0
- (x plus four)(3x minus twelve) equally zero
- x+43x-12=0
- (x+4)(3x-12)=O
-
Similar expressions
- (x-4)(3x-12)=0
- (x+4)(3x+12)=0
(x+4)(3x-12)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 4\right) \left(3 x - 12\right) = 0$$
We get the quadratic equation
$$3 x^{2} - 48 = 0$$
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
$$a = 3$$
$$b = 0$$
$$c = -48$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -4$$
$$\left(x + 4\right) \left(3 x - 12\right) = 0$$
We get the quadratic equation
$$3 x^{2} - 48 = 0$$
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
$$a = 3$$
$$b = 0$$
$$c = -48$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-48) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -4$$
Sum and product of roots
[src]
sum
-4 + 4
$$-4 + 4$$
=
0
$$0$$
product
-4*4
$$- 16$$
=
-16
$$-16$$
-16