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Online solution to the quadratic equation


Result:

Solution calculation of the quadratic equation

For example, enter a=3, b=6, c=-123, d=-126 and e=1080 Click to solve the quadratic equation \(ax^4 + bx^3 + cx^2 + dx + e = 0\)

Quadratic equation : ax4 + bx3 + cx2 + dx + e = 0
Note:
Let p and q be the square roots of any two non-zero numbers

root.
p = sqrt(y1)
q = sqrt(y3)
r = -g / (8pq)
s = b / (4a)
x1 = p + q + r - s
x2 = p - q - r - s
x3 = -p + q - r - s
x4 = -p - q + r - s

Cubic equation:
Discriminate(Δ) = q3 + r2
q = (3c- b2)/9
r = -27d + b(9c-2b2)
s = r + math.sqrt(
Discriminate)
t = r - math.sqrt(
Discriminate)
term1 = math.sqrt(3.0)((-t + s)/2)
r13= 2 * math.sqrt(q)
y1=(- term1 + r13
math.cos(q3/3) )
y2=(- term1 + r13math.cos(q3+(2math.PI)/3) )
y3=(- term1 + r13math.cos(q3+(4math.PI)/3) )

 

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