Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+3x+2=0
-
Equation z^2-6*z+10=0
-
Equation x^2+5x+6=0
-
Equation 1*(x-1)*(x-3)=0
- Express {x} in terms of y where:
- -2*x+20*y=-2
- -20*x-6*y=4
- 6*x+9*y=-9
- -20*x-13*y=15
- Graphing y =:
- x^2
- Limit of the function:
-
x^2
- Derivative of:
-
x^2
-
Identical expressions
- x^ two =- forty-nine
- x squared equally minus 49
- x to the power of two equally minus forty minus nine
- x2=-49
- x²=-49
- x to the power of 2=-49
-
Similar expressions
- 9-4(9+2x)=13
- a^2*(1-x)*(1-a*x+a*x^2)=1
- (9-2x)/(x^2-4x)=(3)/(x-4)+(6)/(x)
- -x^2+8x+6=0
- x^2-4*x+8+2-3*x=0
- a^2*x^2+a*x-21*a+1=0
- x^2=+49
x^2=-49 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
$$x^{2} = -49$$
to
$$x^{2} + 49 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 49$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 7 i$$
$$x_{2} = - 7 i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -49$$
to
$$x^{2} + 49 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 49$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (49) = -196
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
$$x_{1} = 7 i$$
$$x_{2} = - 7 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 49$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 49$$
Sum and product of roots
[src]
sum
-7*I + 7*I
$$- 7 i + 7 i$$
=
0
$$0$$
product
-7*I*7*I
$$- 7 i 7 i$$
=
49
$$49$$
49
The graph