Mister Exam
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How to use it?
- Equation:
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Equation 0*x=0
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Equation x^2=0
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Equation sin(x)=-√3/2
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Equation (x+10)(-x-8)=0
- Express {x} in terms of y where:
- 18*x+14*y=-11
- -5*x+6*y=19
- 4*x+16*y=6
- -6*x+1*y=14
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Identical expressions
- (x+ ten)(-x- eight)= zero
- (x plus 10)( minus x minus 8) equally 0
- (x plus ten)( minus x minus eight) equally zero
- x+10-x-8=0
- (x+10)(-x-8)=O
-
Similar expressions
- (x-10)(-x-8)=0
- (x+10)(-x+8)=0
- (x+10)(x-8)=0
(x+10)(-x-8)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- x - 8\right) \left(x + 10\right) = 0$$
We get the quadratic equation
$$- x^{2} - 18 x - 80 = 0$$
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
$$a = -1$$
$$b = -18$$
$$c = -80$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -10$$
$$x_{2} = -8$$
$$\left(- x - 8\right) \left(x + 10\right) = 0$$
We get the quadratic equation
$$- x^{2} - 18 x - 80 = 0$$
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
$$a = -1$$
$$b = -18$$
$$c = -80$$
, then
D = b^2 - 4 * a * c =
(-18)^2 - 4 * (-1) * (-80) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -10$$
$$x_{2} = -8$$
Sum and product of roots
[src]
sum
-10 - 8
$$-10 - 8$$
=
-18
$$-18$$
product
-10*(-8)
$$- -80$$
=
80
$$80$$
80
The graph