Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation x^2=-16
-
Equation sin(x)=-1/5
- Express {x} in terms of y where:
- 16*x-17*y=-9
- 7*x-2*y=20
- -7*x-7*y=-14
- -15*x+17*y=13
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
- Sum of series:
-
-16
- Limit of the function:
-
-16
-
Identical expressions
- x^ two =- sixteen
- x squared equally minus 16
- x to the power of two equally minus sixteen
- x2=-16
- x²=-16
- x to the power of 2=-16
-
Similar expressions
- x^2=+16
- sqrt(9-x^2)=sqrt(x+9)
- x^2-3=0
- (15x-1)(6x+1,2)=0
- ((65(cosx)^2)+63cosx)/(63(tgx)-16)=0
x^2=-16 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} = -16$$
to
$$x^{2} + 16 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 16$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 4 i$$
$$x_{2} = - 4 i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -16$$
to
$$x^{2} + 16 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (16) = -64
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
$$x_{1} = 4 i$$
$$x_{2} = - 4 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 16$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 16$$
Sum and product of roots
[src]
sum
-4*I + 4*I
$$- 4 i + 4 i$$
=
0
$$0$$
product
-4*I*4*I
$$- 4 i 4 i$$
=
16
$$16$$
16
The graph