If the polynomial $$ax^{4} + bx^{3} + 3x^{2} - 4x - 4$$ is divisible by $$(x^{2} - 1)$$ then $$(a, b) =$$

SolutionsThe Polynomial is divisible by ( x² -1 ), so it will have ( x² -1 ) as one of its factors.

Also, ( x² -1 ) = (x+1)(x-1)

So both +1 and - 1 will be the roots of the polynomial.

Hence f(1) and f(-1) will be equal to 0.

f(1) = a(1) + b (1) + 3 (1) - 4 - 4 = a + b + 3 - 4 - 4 = a + b - 5 = 0 ….(i)

f(1) = a(1) + b (-1) + 3 (1) + 4 - 4 = a - b + 3 = 0 ……..(ii)

On solving (i) and (ii)

a = 1 and b = 4 .Hence Answer (1,4)