Question

Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions. See Example 4. 5) Zeros of 2 f (x) = - 3 and 5: f(3) = 6

Answer 1

Ang o a polynomial of deg We have given with Zero 06 2, -3, 5, and f(3) = -6 let fla) - 923+ 622+ cx td -0 In roots form flx) = a (2-2) (x-1)(x-7) We have x=2, B=-3, v=s a flx = a (2-2) (X - (-3)) 12-5) flay = a (x-2) 18+3) (x-3) Now put a=3 as f13)=-6 + f(3) = al 3-2) 13+3)(3-5) = -6 all (61-2) = -6 9= { put value a = 16 in equation (1) q flx) = { (2-2) (x+3)(3-5) - Į (&?+x-6) 12-5) = { (2? +22-62 -52254 +30) = {(x3–422 – 1/2+30) a theo 2 - - 222 - 1 Latis Hence we get 32 order polynomial as fix)= x - 2x2 - 4x + 15