Solving Higher Order Polynomial Equations (cubic, quartic, quintic)
By DarthVader
Date: 2022-10-16
Topic: 171 see comments
Post views: 975
Solving Higher Order Polynomial Equations (cubic, quartic, quintic)
Let’s consider this example :
Solve : x3 + x2 – 42x = 0
First factor out an x:
x (x2 + x – 42) = 0 . . . . . . . .(1)
This gives us a quadratic expression, which factorises further to give :
x2 + x – 42 = (x + 7) (x – 6)
Substituting back into (1) above, we obtain :
x (x + 7) (x – 6) = 0
So, the solutions are :
x = 0,
x + 7 = 0, x = – 7
x – 6 = 0, x = 6
This curve would intercept the x-axis at x = – 7, x = 0 and x = 6, and the y-intercept is y = 0
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