Mister Exam
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Identical expressions
- two x- seventy-four -x^2= zero
- 2x minus 74 minus x squared equally 0
- two x minus seventy minus four minus x squared equally zero
- 2x-74-x2=0
- 2x-74-x²=0
- 2x-74-x to the power of 2=0
- 2x-74-x^2=O
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Similar expressions
- 2x-74+x^2=0
- 2x+74-x^2=0
2x-74-x^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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
$$a = -1$$
$$b = 2$$
$$c = -74$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 1 - \sqrt{73} i$$
$$x_{2} = 1 + \sqrt{73} i$$
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
$$a = -1$$
$$b = 2$$
$$c = -74$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (-1) * (-74) = -292
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
$$x_{1} = 1 - \sqrt{73} i$$
$$x_{2} = 1 + \sqrt{73} i$$
Vieta's Theorem
rewrite the equation
$$- x^{2} + \left(2 x - 74\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x + 74 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 74$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 74$$
$$- x^{2} + \left(2 x - 74\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x + 74 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 74$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 74$$
Rapid solution
[src]
____ x1 = 1 - I*\/ 73
$$x_{1} = 1 - \sqrt{73} i$$
____ x2 = 1 + I*\/ 73
$$x_{2} = 1 + \sqrt{73} i$$
x2 = 1 + sqrt(73)*i
Sum and product of roots
[src]
sum
____ ____ 1 - I*\/ 73 + 1 + I*\/ 73
$$\left(1 - \sqrt{73} i\right) + \left(1 + \sqrt{73} i\right)$$
=
2
$$2$$
product
/ ____\ / ____\ \1 - I*\/ 73 /*\1 + I*\/ 73 /
$$\left(1 - \sqrt{73} i\right) \left(1 + \sqrt{73} i\right)$$
=
74
$$74$$
74
Numerical answer
[src]
x1 = 1.0 - 8.54400374531753*i
x2 = 1.0 + 8.54400374531753*i
x2 = 1.0 + 8.54400374531753*i