Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) %3D хе 4х, а%3D 0 Тз(x) x – 4x² + 16x° 2

Q9. (a) (i) (ii) Calculate (2 + i√5)(√5 - i). Hence verify that (√5 - i) is a root of the equation (2 + i√5)z = 3z* where z* is the conjugate of z.

Determine an approximate value of f(1.22) utilizing Lagrange interpolating polynomial of degree four if f(1.15) = -0.835, f(1.20) = -0.470, f(1.25) = -0.094, f(1.30)= 0.291 and f(1.35) = 0.683.

A quadratic polynomial y = 4x2 + 7x – 3 has roots p and q. Find a quadratic g(x) = x + ax + B with roots r = .2 1 and S = O a. g(x) = x² - O b. g(x) = x² - 7x а. 3 7x 3 Ос. g(x) = 7x x + 3 - 7x d. O d. g(x) = x²+ 3 +/M 4/3 4|m 4/3 + +