a. Plot the zeros of each polynomial on a line together with the zeros of its first derivative.

i) y = x² - 4ii) y = x² + 8x + 15iii) y = x³ - 3x² + 4 = (x + 1)(x - 2)²iv) y = x³ - 33x² + 216x = x(x - 9)(x - 24)

b. Use Rolle’s Theorem to prove that between every two zeros of

Transcribed Image Text:

xn + an-1.xn-1 + + a₁x + ao there lies a zero of + a₁. ... nxn-1 + (n − 1)an-1x²-2 + - ...