Mister Exam
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How to use it?
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Equation sin(x)=0
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Equation x^3-9*x=0
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- 3*x-17*y=-6
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Identical expressions
- (x- seventeen)(x+ eight)= zero
- (x minus 17)(x plus 8) equally 0
- (x minus seventeen)(x plus eight) equally zero
- x-17x+8=0
- (x-17)(x+8)=O
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Similar expressions
- (x+17)(x+8)=0
- (x-17)(x-8)=0
(x-17)(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
$$\left(x - 17\right) \left(x + 8\right) = 0$$
We get the quadratic equation
$$x^{2} - 9 x - 136 = 0$$
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
$$a = 1$$
$$b = -9$$
$$c = -136$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 17$$
$$x_{2} = -8$$
$$\left(x - 17\right) \left(x + 8\right) = 0$$
We get the quadratic equation
$$x^{2} - 9 x - 136 = 0$$
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
$$a = 1$$
$$b = -9$$
$$c = -136$$
, then
D = b^2 - 4 * a * c =
(-9)^2 - 4 * (1) * (-136) = 625
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 17$$
$$x_{2} = -8$$
Sum and product of roots
[src]
sum
-8 + 17
$$-8 + 17$$
=
9
$$9$$
product
-8*17
$$- 136$$
=
-136
$$-136$$
-136