Research the history of Francois Viete and the theorem. Find the theorem and prove it. (Hint: Start with the fact that m and n are distinct solutions of the quadratic equation x^2+bx+c=0, so m^2+bm+c=0 and n^2+bn+c=0 .) Apply Viete’s Theorem to the general quadratic
equation ax^2+bx+c=0. This results in a Corollary of Viete’s Theorem. State it. If m and n are solutions to the quadratic equation ax^2+bx+c=0 and m+n=-b , then the average of m and n is -b/2. Therefore, let m=-b/2+x and n=-b/2- x . (Do you agree?) Substitute these values into the second part of Viete’s Theorem and solve for x. What is the result? How does this result relate to the quadratic formula? Use the completing the square process to prove the quadratic formula provides solutions for the general quadratic equation ax^2+bx+c=0