Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 1-5*x=-6*x+8
-
Equation 3-3*6+2=x
-
Equation x^2=-25
-
Equation cos(x/2)=-(1/2)
- Express {x} in terms of y where:
- 12*x+14*y=-15
- -9*x-15*y=-4
- 12*x-14*y=20
- -20*x-14*y=5
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
- Limit of the function:
-
-25
-
Identical expressions
- x^ two =- twenty-five
- x squared equally minus 25
- x to the power of two equally minus twenty minus five
- x2=-25
- x²=-25
- x to the power of 2=-25
-
Similar expressions
- x^2=+25
- (x^2-x-20)(x^2-3x-18)=252
- 2*x^4-x^3-6x^2-x+2=0
- (x-2)^5+(4-x)^5=2
- sin(x)^2=1/2
- (5x-2)(5x+2)-(5x-1)^2=4x
- x^2+5x+9=0
x^2=-25 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
$$x^{2} = -25$$
to
$$x^{2} + 25 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 25$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 5 i$$
$$x_{2} = - 5 i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -25$$
to
$$x^{2} + 25 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (25) = -100
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
$$x_{1} = 5 i$$
$$x_{2} = - 5 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 25$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 25$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 25$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 25$$
Sum and product of roots
[src]
sum
-5*I + 5*I
$$- 5 i + 5 i$$
=
0
$$0$$
product
-5*I*5*I
$$- 5 i 5 i$$
=
25
$$25$$
25
The graph