Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation z^3=-i
-
Equation 5^(9-x)=64
-
Equation -x^2-4=0
-
Equation (x+3)^2-16=(1-2x)^2
- Express {x} in terms of y where:
- -8*x+14*y=5
- 17*x+7*y=-6
- -11*x-14*y=6
- -18*x-8*y=-5
- Integral of d{x}:
-
-x^2-4
- Graphing y =:
- -x^2-4
- Factor polynomial:
- -x^2-4
-
Identical expressions
- -x^ two - four = zero
- minus x squared minus 4 equally 0
- minus x to the power of two minus four equally zero
- -x2-4=0
- -x²-4=0
- -x to the power of 2-4=0
- -x^2-4=O
-
Similar expressions
- -x^2+4=0
- x^2-4=0
-x^2-4=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
$$a = -1$$
$$b = 0$$
$$c = -4$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - 2 i$$
$$x_{2} = 2 i$$
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
$$a = -1$$
$$b = 0$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (-4) = -16
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
$$x_{1} = - 2 i$$
$$x_{2} = 2 i$$
Vieta's Theorem
rewrite the equation
$$- x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 4 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 4$$
$$- x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 4 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 4$$
Sum and product of roots
[src]
sum
-2*I + 2*I
$$- 2 i + 2 i$$
=
0
$$0$$
product
-2*I*2*I
$$- 2 i 2 i$$
=
4
$$4$$
4
The graph