Mister Exam

Other calculators

2x+8x^2=0

2x+8x^2=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    
2*x + 8*x  = 0
8x2+2x=08 x^{2} + 2 x = 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=8a = 8
b=2b = 2
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (8) * (0) = 4

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=0x_{1} = 0
x2=−14x_{2} = - \frac{1}{4}
Vieta's Theorem
rewrite the equation
8x2+2x=08 x^{2} + 2 x = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2+x4=0x^{2} + \frac{x}{4} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=14p = \frac{1}{4}
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−14x_{1} + x_{2} = - \frac{1}{4}
x1x2=0x_{1} x_{2} = 0
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.515.010.012.5-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -1/4
x1=−14x_{1} = - \frac{1}{4} 
x2 = 0
x2=0x_{2} = 0 
x2 = 0
Sum and product of roots [src] 
sum
-1/4
−14- \frac{1}{4} 
=
-1/4
−14- \frac{1}{4} 
product
0*(-1)
------
  4
(−1)04\frac{\left(-1\right) 0}{4} 
=
0
00 
0
Numerical answer [src] 
x1 = -0.25
x2 = 0.0
x2 = 0.0
The graph
2x+8x^2=0 equation
    © Mister Exam – Calculator