Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 49*x^3+14*x^2+x=0
-
Equation 9^x-8*3^x-9=0
- Equation x+y=4
-
Equation 5x+8=-12
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- Derivative of:
-
x^2+5
- Integral of d{x}:
-
x^2+5
- Factor polynomial:
- x^2+5
-
Identical expressions
- x^ two + five = zero
- x squared plus 5 equally 0
- x to the power of two plus five equally zero
- x2+5=0
- x²+5=0
- x to the power of 2+5=0
- x^2+5=O
-
Similar expressions
- x^2-5=0
x^2+5=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
$$a = 1$$
$$b = 0$$
$$c = 5$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \sqrt{5} i$$
Simplify
$$x_{2} = - \sqrt{5} i$$
Simplify
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
$$a = 1$$
$$b = 0$$
$$c = 5$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (5) = -20
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
$$x_{1} = \sqrt{5} i$$
Simplify
$$x_{2} = - \sqrt{5} i$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 5$$
Sum and product of roots
[src]
sum
___ ___ 0 - I*\/ 5 + I*\/ 5
$$\left(0 - \sqrt{5} i\right) + \sqrt{5} i$$
=
0
$$0$$
product
___ ___ 1*-I*\/ 5 *I*\/ 5
$$\sqrt{5} i 1 \left(- \sqrt{5} i\right)$$
=
5
$$5$$
5
Rapid solution
[src]
___ x1 = -I*\/ 5
$$x_{1} = - \sqrt{5} i$$
___ x2 = I*\/ 5
$$x_{2} = \sqrt{5} i$$
The graph