Mister Exam
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Identical expressions
- x^ two + thirteen *x+ two hundred and ninety-five , three = zero
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Similar expressions
- x^2+13*x-295,3=0
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x^2+13*x+295,3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2953
x + 13*x + ---- = 0
10
$$\left(x^{2} + 13 x\right) + \frac{2953}{10} = 0$$
Detail solution
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
$$a = 1$$
$$b = 13$$
$$c = \frac{2953}{10}$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{13}{2} + \frac{\sqrt{25305} i}{10}$$
$$x_{2} = - \frac{13}{2} - \frac{\sqrt{25305} i}{10}$$
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
$$a = 1$$
$$b = 13$$
$$c = \frac{2953}{10}$$
, then
D = b^2 - 4 * a * c =
(13)^2 - 4 * (1) * (2953/10) = -5061/5
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{13}{2} + \frac{\sqrt{25305} i}{10}$$
$$x_{2} = - \frac{13}{2} - \frac{\sqrt{25305} i}{10}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 13$$
$$q = \frac{c}{a}$$
$$q = \frac{2953}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -13$$
$$x_{1} x_{2} = \frac{2953}{10}$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 13$$
$$q = \frac{c}{a}$$
$$q = \frac{2953}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -13$$
$$x_{1} x_{2} = \frac{2953}{10}$$
Rapid solution
[src]
_______
13 I*\/ 25305
x1 = - -- - -----------
2 10
$$x_{1} = - \frac{13}{2} - \frac{\sqrt{25305} i}{10}$$
_______
13 I*\/ 25305
x2 = - -- + -----------
2 10
$$x_{2} = - \frac{13}{2} + \frac{\sqrt{25305} i}{10}$$
x2 = -13/2 + sqrt(25305)*i/10
Sum and product of roots
[src]
sum
_______ _______ 13 I*\/ 25305 13 I*\/ 25305 - -- - ----------- + - -- + ----------- 2 10 2 10
$$\left(- \frac{13}{2} - \frac{\sqrt{25305} i}{10}\right) + \left(- \frac{13}{2} + \frac{\sqrt{25305} i}{10}\right)$$
=
-13
$$-13$$
product
/ _______\ / _______\ | 13 I*\/ 25305 | | 13 I*\/ 25305 | |- -- - -----------|*|- -- + -----------| \ 2 10 / \ 2 10 /
$$\left(- \frac{13}{2} - \frac{\sqrt{25305} i}{10}\right) \left(- \frac{13}{2} + \frac{\sqrt{25305} i}{10}\right)$$
=
2953 ---- 10
$$\frac{2953}{10}$$
2953/10
Numerical answer
[src]
x1 = -6.5 + 15.9075453794732*i
x2 = -6.5 - 15.9075453794732*i
x2 = -6.5 - 15.9075453794732*i