Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=1/5
-
Equation x^2+11=0
-
Equation x^2+5x+6=0
-
Equation -x/7+x=15/7
- Express {x} in terms of y where:
- 9*x+17*y=13
- 20*x+18*y=-9
- -4*x-8*y=-20
- -1*x+4*y=-10
- Integral of d{x}:
- x^2+11
-
Identical expressions
- x^ two + eleven = zero
- x squared plus 11 equally 0
- x to the power of two plus eleven equally zero
- x2+11=0
- x²+11=0
- x to the power of 2+11=0
- x^2+11=O
-
Similar expressions
- x^2-11=0
x^2+11=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
$$a = 1$$
$$b = 0$$
$$c = 11$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \sqrt{11} i$$
$$x_{2} = - \sqrt{11} i$$
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
$$a = 1$$
$$b = 0$$
$$c = 11$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (11) = -44
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
$$x_{1} = \sqrt{11} i$$
$$x_{2} = - \sqrt{11} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 11$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 11$$
Rapid solution
[src]
____ x1 = -I*\/ 11
$$x_{1} = - \sqrt{11} i$$
____ x2 = I*\/ 11
$$x_{2} = \sqrt{11} i$$
x2 = sqrt(11)*i
Sum and product of roots
[src]
sum
____ ____ - I*\/ 11 + I*\/ 11
$$- \sqrt{11} i + \sqrt{11} i$$
=
0
$$0$$
product
____ ____ -I*\/ 11 *I*\/ 11
$$- \sqrt{11} i \sqrt{11} i$$
=
11
$$11$$
11
The graph