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Identical expressions
- three (x− fifteen)(x+ five , seven)= zero .
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- three (x− fifteen)(x plus five , seven) equally zero .
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Similar expressions
- 3(x−15)(x-5,7)=0.
3(x−15)(x+5,7)=0. equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 57\
3*(x - 15)*|x + --| = 0
\ 10/
$$3 \left(x - 15\right) \left(x + \frac{57}{10}\right) = 0$$
Detail solution
Expand the expression in the equation
$$3 \left(x - 15\right) \left(x + \frac{57}{10}\right) = 0$$
We get the quadratic equation
$$3 x^{2} - \frac{279 x}{10} - \frac{513}{2} = 0$$
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
$$a = 3$$
$$b = - \frac{279}{10}$$
$$c = - \frac{513}{2}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 15$$
$$x_{2} = - \frac{57}{10}$$
$$3 \left(x - 15\right) \left(x + \frac{57}{10}\right) = 0$$
We get the quadratic equation
$$3 x^{2} - \frac{279 x}{10} - \frac{513}{2} = 0$$
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
$$a = 3$$
$$b = - \frac{279}{10}$$
$$c = - \frac{513}{2}$$
, then
D = b^2 - 4 * a * c =
(-279/10)^2 - 4 * (3) * (-513/2) = 385641/100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 15$$
$$x_{2} = - \frac{57}{10}$$
Sum and product of roots
[src]
sum
57
15 - --
10
$$- \frac{57}{10} + 15$$
=
93 -- 10
$$\frac{93}{10}$$
product
15*(-57) -------- 10
$$\frac{\left(-57\right) 15}{10}$$
=
-171/2
$$- \frac{171}{2}$$
-171/2