Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+7=0
-
Equation x+2=0
-
Equation 2x=0
-
Equation (x-1)(-x-4)=0
- Express {x} in terms of y where:
- -15*x-13*y=-20
- -15*x-19*y=2
- 4*x+4*y=13
- -4*x+14*y=-2
-
Identical expressions
- 7x^ two -6x+ two = zero
- 7x squared minus 6x plus 2 equally 0
- 7x to the power of two minus 6x plus two equally zero
- 7x2-6x+2=0
- 7x²-6x+2=0
- 7x to the power of 2-6x+2=0
- 7x^2-6x+2=O
-
Similar expressions
- 7x^2-6x-2=0
- 7x^2+6x+2=0
7x^2-6x+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
$$a = 7$$
$$b = -6$$
$$c = 2$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{3}{7} + \frac{\sqrt{5} i}{7}$$
$$x_{2} = \frac{3}{7} - \frac{\sqrt{5} i}{7}$$
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
$$a = 7$$
$$b = -6$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (7) * (2) = -20
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
$$x_{1} = \frac{3}{7} + \frac{\sqrt{5} i}{7}$$
$$x_{2} = \frac{3}{7} - \frac{\sqrt{5} i}{7}$$
Vieta's Theorem
rewrite the equation
$$\left(7 x^{2} - 6 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{6 x}{7} + \frac{2}{7} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{6}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{2}{7}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6}{7}$$
$$x_{1} x_{2} = \frac{2}{7}$$
$$\left(7 x^{2} - 6 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{6 x}{7} + \frac{2}{7} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{6}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{2}{7}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6}{7}$$
$$x_{1} x_{2} = \frac{2}{7}$$
Rapid solution
[src]
___
3 I*\/ 5
x1 = - - -------
7 7
$$x_{1} = \frac{3}{7} - \frac{\sqrt{5} i}{7}$$
___
3 I*\/ 5
x2 = - + -------
7 7
$$x_{2} = \frac{3}{7} + \frac{\sqrt{5} i}{7}$$
x2 = 3/7 + sqrt(5)*i/7
Sum and product of roots
[src]
sum
___ ___ 3 I*\/ 5 3 I*\/ 5 - - ------- + - + ------- 7 7 7 7
$$\left(\frac{3}{7} - \frac{\sqrt{5} i}{7}\right) + \left(\frac{3}{7} + \frac{\sqrt{5} i}{7}\right)$$
=
6/7
$$\frac{6}{7}$$
product
/ ___\ / ___\ |3 I*\/ 5 | |3 I*\/ 5 | |- - -------|*|- + -------| \7 7 / \7 7 /
$$\left(\frac{3}{7} - \frac{\sqrt{5} i}{7}\right) \left(\frac{3}{7} + \frac{\sqrt{5} i}{7}\right)$$
=
2/7
$$\frac{2}{7}$$
2/7
Numerical answer
[src]
x1 = 0.428571428571429 + 0.31943828249997*i
x2 = 0.428571428571429 - 0.31943828249997*i
x2 = 0.428571428571429 - 0.31943828249997*i
The graph