Mister Exam

Other calculators

x^2+3x+4=0

x^2+3x+4=0 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  + 3*x + 4 = 0
(x2+3x)+4=0\left(x^{2} + 3 x\right) + 4 = 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=3b = 3
c=4c = 4
, then
D = b^2 - 4 * a * c = 

(3)^2 - 4 * (1) * (4) = -7

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=−32+7i2x_{1} = - \frac{3}{2} + \frac{\sqrt{7} i}{2}
x2=−32−7i2x_{2} = - \frac{3}{2} - \frac{\sqrt{7} i}{2}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=3p = 3
q=caq = \frac{c}{a}
q=4q = 4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−3x_{1} + x_{2} = -3
x1x2=4x_{1} x_{2} = 4
The graph
0123-8-7-6-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
          ___             ___
  3   I*\/ 7      3   I*\/ 7 
- - - ------- + - - + -------
  2      2        2      2
(−32−7i2)+(−32+7i2)\left(- \frac{3}{2} - \frac{\sqrt{7} i}{2}\right) + \left(- \frac{3}{2} + \frac{\sqrt{7} i}{2}\right) 
=
-3
−3-3 
product
/          ___\ /          ___\
|  3   I*\/ 7 | |  3   I*\/ 7 |
|- - - -------|*|- - + -------|
\  2      2   / \  2      2   /
(−32−7i2)(−32+7i2)\left(- \frac{3}{2} - \frac{\sqrt{7} i}{2}\right) \left(- \frac{3}{2} + \frac{\sqrt{7} i}{2}\right) 
=
4
44 
4
Rapid solution [src] 
               ___
       3   I*\/ 7 
x1 = - - - -------
       2      2
x1=−32−7i2x_{1} = - \frac{3}{2} - \frac{\sqrt{7} i}{2} 
               ___
       3   I*\/ 7 
x2 = - - + -------
       2      2
x2=−32+7i2x_{2} = - \frac{3}{2} + \frac{\sqrt{7} i}{2} 
x2 = -3/2 + sqrt(7)*i/2
Numerical answer [src] 
x1 = -1.5 - 1.3228756555323*i
x2 = -1.5 + 1.3228756555323*i
x2 = -1.5 + 1.3228756555323*i
The graph
x^2+3x+4=0 equation
    © Mister Exam – Calculator