Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 0,4(x-3)-1,6=5(0,1x-0,5)
-
Equation x-243=x/2-51
-
Equation x^3-2*x^2+x+3=0
-
Equation 2*sin(x)-3*cos(x)=0
- Express {x} in terms of y where:
- 5*x-15*y=13
- 18*x-15*y=-7
- 14*x-4*y=14
- 13*x+12*y=7
- Integral of d{x}:
- x^2+4x+13
-
Identical expressions
- x^ two +4x+ thirteen = zero
- x squared plus 4x plus 13 equally 0
- x to the power of two plus 4x plus thirteen equally zero
- x2+4x+13=0
- x²+4x+13=0
- x to the power of 2+4x+13=0
- x^2+4x+13=O
-
Similar expressions
- x^2-4x+13=0
- x^2+4x-13=0
x^2+4x+13=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
$$a = 1$$
$$b = 4$$
$$c = 13$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = -2 + 3 i$$
$$x_{2} = -2 - 3 i$$
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
$$a = 1$$
$$b = 4$$
$$c = 13$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (13) = -36
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
$$x_{1} = -2 + 3 i$$
$$x_{2} = -2 - 3 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 13$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 13$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 13$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 13$$
Rapid solution
[src]
x1 = -2 - 3*I
$$x_{1} = -2 - 3 i$$
x2 = -2 + 3*I
$$x_{2} = -2 + 3 i$$
x2 = -2 + 3*i
Sum and product of roots
[src]
sum
-2 - 3*I + -2 + 3*I
$$\left(-2 - 3 i\right) + \left(-2 + 3 i\right)$$
=
-4
$$-4$$
product
(-2 - 3*I)*(-2 + 3*I)
$$\left(-2 - 3 i\right) \left(-2 + 3 i\right)$$
=
13
$$13$$
13
The graph