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Find the values of a and b, if x2 − 4 is a factor of ax4 +2x3 -3x2 +bx -4.

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Let f(x) = ax4 +2x3 -3x2 +bx -4 and g(x) = x2 -4

We have g(x) = x2 − 4 = (x-4) (x+2)

Given g(x) is a factor of f(x).

(x-2) and (x+2) are factors of f(x)

From factor theorem,

If (x-2) and (x+2) are factor of f(x) then f(2) = 0 and f(-2) = 0 respectively

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