Mister Exam
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Identical expressions
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Similar expressions
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-13.7x*(x-5.8)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
-137*x ------*(x - 29/5) = 0 10
$$- \frac{137 x}{10} \left(x - \frac{29}{5}\right) = 0$$
Detail solution
Expand the expression in the equation
$$- \frac{137 x}{10} \left(x - \frac{29}{5}\right) = 0$$
We get the quadratic equation
$$- \frac{137 x^{2}}{10} + \frac{3973 x}{50} = 0$$
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
$$a = - \frac{137}{10}$$
$$b = \frac{3973}{50}$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = \frac{29}{5}$$
$$- \frac{137 x}{10} \left(x - \frac{29}{5}\right) = 0$$
We get the quadratic equation
$$- \frac{137 x^{2}}{10} + \frac{3973 x}{50} = 0$$
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
$$a = - \frac{137}{10}$$
$$b = \frac{3973}{50}$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(3973/50)^2 - 4 * (-137/10) * (0) = 15784729/2500
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = \frac{29}{5}$$
Sum and product of roots
[src]
sum
29/5
$$\frac{29}{5}$$
=
29/5
$$\frac{29}{5}$$
product
0*29 ---- 5
$$\frac{0 \cdot 29}{5}$$
=
0
$$0$$
0