One classical method for solving cubics is Cardano's solution. The cubic equation r3+ar2+br-c = 0 is transformed to a reduced form y3+py+q = 0 by the substitution x = y . The coefficients in the reduced form are p = b- A real root of the reduced form is given by yl = [2 +ji +--ji, where s = (5). (3) 21 2. Then a real root of the original equation is given by yi-3. The other two roots can be found by similar formulas or by factoring out r (deflating r1) and solving the resulting quadratic equation Using Matlab do the following: (a) Apply Cardano's method to find the real root of r3+3r2+8 +380, for various values of . Investigate the loss of accuracy from roundoff for large = 1010:19 observe the results when is about the reciprocal of machine unit /Hint: You can use Matlab's "eps" for this]. (b) Apply Newton's method to the same equation for the same values of . Investigate the effects of roundoff error and the choice of starting value. Explain the rapid convergence of Newton's method for very large One classical method for solving cubics is Cardano's solution. The cubic equation r3+ar2+br-c = 0 is transformed to a reduced form y3+py+q = 0 by the substitution x = y . The coefficients in the reduced form are p = b- A real root of the reduced form is given by yl = [2 +ji +--ji, where s = (5). (3) 21 2. Then a real root of the original equation is given by yi-3. The other two roots can be found by similar formulas or by factoring out r (deflating r1) and solving the resulting quadratic equation Using Matlab do the following: (a) Apply Cardano's method to find the real root of r3+3r2+8 +380, for various values of . Investigate the loss of accuracy from roundoff for large = 1010:19 observe the results when is about the reciprocal of machine unit /Hint: You can use Matlab's "eps" for this]. (b) Apply Newton's method to the same equation for the same values of . Investigate the effects of roundoff error and the choice of starting value. Explain the rapid convergence of Newton's method for very large