Question

Find the values of a and b so that (z+1) and (z-1) are factors of z^4+ az^3 + 2z^2-3z+b

Answer 1

if z+1 and z-1 are the factors of this polynomial then the product of these two factors is also the factor of it.
so multiply z+1 and z-1 and then divide it by this polynomial.
at last a remainder is left with both the terms a and b. 
find the vale of a and b by subsitution method or any method. 


hope this will help you.

Answer 2

Sol: if x2- 4 is a factor of ax4+ 2x3- 3x2+ bx - 4. x2 - 4 = 0 ⇒ x = ±2 are zeros of the polynomial p(x) = ax4+ 2x3- 3x2+ bx - 4. ∴ p(2) = 0 and p(-2) = 0. p(2) = 0 then 16a + 16 -12 +2b -4 = 0 16a + 2b  = 0 -------------(1)p(-2) = 0 then 16a -16 -12 - 2b - 4 = 0 16a -2b = 32 -------------(2) Substract (2) from (1) we get 4b = -32 b = -8 Substitute b is in equ(1) we get 16a - 16 = 0 ∴ a = 1 and b = -8.


Hope it will help you