Simultaneous Equations Finding the Intersection of a Cubic and a QuadraticMy functions arey=−0.65(x−8.165)2+1.5(x−8.165)+6.872y=0.08(x−11)3−2.2(x−11)+5.9By using simultaneous equations and equating the functions to one another I've simplified it to the point where:0.08x3−1.99x2+14.7255x−27.608=0This 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=11.03536And 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.

Question

Simultaneous Equations Finding the Intersection of a Cubic and a QuadraticMy functions arey=−0.65(x−8.165)2+1.5(x−8.165)+6.872y=0.08(x−11)3−2.2(x−11)+5.9By using simultaneous equations and equating the functions to one another I&#039;ve simplified it to the point where:0.08x3−1.99x2+14.7255x−27.608=0This 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=11.03536And although this helped me greatly, for the assignment I&#039;m doing I won&#039;t be marked on using that method as we haven&#039;t been taught it and it&#039;s not on the criteria.I&#039;m just wondering if there is another method I can use that would get the same results.

Waylon Padilla · Accepted Answer

You know that you have three real roots.Using whole numbers, your cubic equation write225x3−199100x2+294512000x−22136643800000=0xk=19924+1912595cos⁡(2kπ3−13cos−1(−694979394046810295))with k=0,1,2.

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

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