Consider the polynomial p(x) = 2x^4 + 5x^3 - 3.5x^2 - 4x - 1.5 which has two real zeros x1 element( infinity, -2.5 ) an
Posted: Tue Sep 07, 2021 7:56 am
Consider the polynomial
p(x) = 2x^4 + 5x^3 - 3.5x^2 - 4x - 1.5
which has two real zeros x1 element( infinity, -2.5 ) and x2 element [ 0.5, infinity)
Question 1.
Use the bisection method to approximate the zeros x1 and x2 of p(x) within a tolerance of 10^-6
Question 2.
If p(x)=(x-x1)q1(x), where x1 is the approximate zero rounded to three decimals obtained in question 1, determine the polynomial q1(x)
Question 3.
If q1(x)=(x-x2) q2(x), where x2 is the approximate zero rounded to three decimals obtained in question 1, determine the polynomial q2(x). Use the full values of the coefficients of the polynomial q1(x), and give the values of the coefficients of q2(x) rounded to three decimals
Question 4.
Deduce an approximate value of the complex root x3=α + β j (lying in the second quadrant in the complex plane) of the polynomial p(x) within a tolerance of 10^-6 when using the deflation and bisection method. Use the full values of the coefficients of the polynomials above, and give the values of α and β rounded to three decimals
p(x) = 2x^4 + 5x^3 - 3.5x^2 - 4x - 1.5
which has two real zeros x1 element( infinity, -2.5 ) and x2 element [ 0.5, infinity)
Question 1.
Use the bisection method to approximate the zeros x1 and x2 of p(x) within a tolerance of 10^-6
Question 2.
If p(x)=(x-x1)q1(x), where x1 is the approximate zero rounded to three decimals obtained in question 1, determine the polynomial q1(x)
Question 3.
If q1(x)=(x-x2) q2(x), where x2 is the approximate zero rounded to three decimals obtained in question 1, determine the polynomial q2(x). Use the full values of the coefficients of the polynomial q1(x), and give the values of the coefficients of q2(x) rounded to three decimals
Question 4.
Deduce an approximate value of the complex root x3=α + β j (lying in the second quadrant in the complex plane) of the polynomial p(x) within a tolerance of 10^-6 when using the deflation and bisection method. Use the full values of the coefficients of the polynomials above, and give the values of α and β rounded to three decimals