Simultaneous Equations Finding the Intersection of a Cubic and a Quadratic My functions are

Ezequiel Olson

Ezequiel Olson

Answered question

2022-04-24

Simultaneous Equations Finding the Intersection of a Cubic and a Quadratic
My functions are
y=0.65(x8.165)2+1.5(x8.165)+6.872
y=0.08(x11)32.2(x11)+5.9
By using simultaneous equations and equating the functions to one another I've simplified it to the point where:
0.08x31.99x2+14.7255x27.608=0
This had me stuck for a while but when I looked it up online I found I could use the Newton - Raphson Method to solve it.
I got the intercepts: x=2.85281,x=10.98682,x=11.03536
And although this helped me greatly, for the assignment I'm doing I won't be marked on using that method as we haven't been taught it and it's not on the criteria.
I'm just wondering if there is another method I can use that would get the same results.

Answer & Explanation

Waylon Padilla

Waylon Padilla

Beginner2022-04-25Added 19 answers

You know that you have three real roots.
Using whole numbers, your cubic equation write
225x3199100x2+294512000x22136643800000=0
xk=19924+1912595cos(2kπ313cos1(694979394046810295))
with k=0,1,2.

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