Mister Exam

Other calculators

x^2+2x+5

x^2+2x+5 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
 2              
x  + 2*x + 5 = 0
x2+2x+5=0x^{2} + 2 x + 5 = 0
Simplify
Detail solution
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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=2b = 2
c=5c = 5
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (5) = -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
x1=−1+2ix_{1} = -1 + 2 i
Simplify
x2=−1−2ix_{2} = -1 - 2 i
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=2p = 2
q=caq = \frac{c}{a}
q=5q = 5
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−2x_{1} + x_{2} = -2
x1x2=5x_{1} x_{2} = 5
The graph
01234-7-6-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 + -1 - 2*I + -1 + 2*I
(0−(1+2i))−(1−2i)\left(0 - \left(1 + 2 i\right)\right) - \left(1 - 2 i\right) 
=
-2
−2-2 
product
1*(-1 - 2*I)*(-1 + 2*I)
1(−1−2i)(−1+2i)1 \left(-1 - 2 i\right) \left(-1 + 2 i\right) 
=
5
55 
5
Rapid solution [src] 
x1 = -1 - 2*I
x1=−1−2ix_{1} = -1 - 2 i
Simplify 
x2 = -1 + 2*I
x2=−1+2ix_{2} = -1 + 2 i
Simplify
Numerical answer [src] 
x1 = -1.0 - 2.0*i
x2 = -1.0 + 2.0*i
x2 = -1.0 + 2.0*i
The graph
x^2+2x+5 equation
    © Mister Exam – Calculator