Question

find the value of 'a' and 'b' if x^2 - 4 is a factor of ax^4 + 2x^3 - 3x^2 +bx +4.
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Answer 1

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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 = 016a + 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.

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