Answer :
Answer:
Follow me
Step-by-step explanation:
6x6 - 35x5 + 56x4 - 56x2 + 35x - 6 = 0 Let P(x) = 6x6 - 35x5 + 56x4 - 56x2 + 35x - 6 ∵ ∵ P(1) = 6 - 35 + 56 - 56 +35 - 6 = 0 P(-1) = 6 + 35 +56 - 56 -35 - 6 = 0 ∴ ∴ (x - 1) (x + 1) are factors of P(x). ⇒ (x2 - 1) is a factor of P(x). Now, 6x2- 35x5 + 56x4 - 56x2 + 35x - 6 = (x2 - 1)(6x4 - 35x3 + 62x2 - 35x + 6) Let g(x) = 6x4 - 35x3 + 62x2 - 35x + 6 g(2) = 6 x 16 -35 x 8 + 62 x 4 - 35 x 2 + 6 = 96 - 280+ 248 - 70 + 6 = 350 - 350 = 0 Also g(3) = 6 x 81 - 35 x 27 + 62 x 9 - 35 x 3 + 6 = 486 -945 +558 -105 + 6 = 1050 - 1050 = 0 Hence, (x - 2)(x - 3) is factor of g(x) ∴ ∴ g(x) = (x - 2)(x - 3) (6x2 + 5x + 1) ∴ ∴ P(x) = (x - 1)(x + 1) (x - 2) (x - 3) (6x2 - 5x + 1) P(x) = (x - 1) (x +1) (x - 2) (x - 3) (2x - 1) (3x - 1) ∴ ∴ Roots of given equation are 1, -1, 2, 3, 1/2 & 1/3Read more on Sarthaks.com - https://www.sarthaks.com/2264266/solve-6-x-6-35-x-5-56-x-4-56-x-2-35-x-6-0