Given the equation: x3−4x=0 transform Take common factor x from the equation we get: x(x2−4)=0 then: x1=0 and also we get the equation x2−4=0 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: x2=2aD−b x3=2a−D−b where D = b^2 - 4*a*c - it is the discriminant. Because a=1 b=0 c=−4 , then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-4) = 16
Because D > 0, then the equation has two roots.
x2 = (-b + sqrt(D)) / (2*a)
x3 = (-b - sqrt(D)) / (2*a)
or x2=2 x3=−2 The final answer for x^3 - 4*x = 0: x1=0 x2=2 x3=−2
Vieta's Theorem
it is reduced cubic equation px2+qx+v+x3=0 where p=ab p=0 q=ac q=−4 v=ad v=0 Vieta Formulas x1+x2+x3=−p x1x2+x1x3+x2x3=q x1x2x3=v x1+x2+x3=0 x1x2+x1x3+x2x3=−4 x1x2x3=0