Consider the cubic polynomial equation f(x) 3-44 2+564 1728 0. 1. Prove that equation (1) has three real roots, by exhibiting three sign change inter- vals, one for each root 2eote by . the the real roots of equation (1) ,p2:fa the three real roots of equation In this part you will need to use Vieta's formulae http://mathworld.wolfram.com/VietasFormulas.html Vieta's formulae allow one to express certain functions of the roots of a polynomial in terms of its coefficients, without having to compute the roots (a) Compute the exact values of the sum + p2 + 3 and the product pipp3 (b) Compute the eract value of the 2elementary symmetric function pip2 nd P2P3 + P1P3 (c) Compute the exact values of the sums + + and 1 + + (d) Compute the exact value of the quantity 2 + 2 +