Mister Exam
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How to use it?
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Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
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Identical expressions
- (x+ twenty)*(-x+ ten)= zero
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Similar expressions
- (x+20)(-x+10)=0
- (x+20)*(-x-10)=0
- (x+20)(-x+10)
- (x-20)*(-x+10)=0
- (x+20)*(x+10)=0
(x+20)*(-x+10)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(10 - x\right) \left(x + 20\right) = 0$$
We get the quadratic equation
$$- x^{2} - 10 x + 200 = 0$$
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
$$a = -1$$
$$b = -10$$
$$c = 200$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -20$$
$$x_{2} = 10$$
$$\left(10 - x\right) \left(x + 20\right) = 0$$
We get the quadratic equation
$$- x^{2} - 10 x + 200 = 0$$
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
$$a = -1$$
$$b = -10$$
$$c = 200$$
, then
D = b^2 - 4 * a * c =
(-10)^2 - 4 * (-1) * (200) = 900
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -20$$
$$x_{2} = 10$$
Sum and product of roots
[src]
sum
-20 + 10
$$-20 + 10$$
=
-10
$$-10$$
product
-20*10
$$- 200$$
=
-200
$$-200$$
-200