AP ICET 2nd May 2018 Shift-2

Question 123

If $$x^2 - 4$$ divides $$x^4 + ax^3 + bx^2 - 5x + 4$$ then $$a - b =$$

Solution

It means that both (x-2) and (x+2) are factors of $$x^4 + ax^3 + bx^2 - 5x + 4$$

This implies that $$x^4 + ax^3 + bx^2 - 5x + 4$$ at x = 2 is 0 
i.e. 4a + 2b = -5

Also, it implies that $$x^4 + ax^3 + bx^2 - 5x + 4$$ at x = -2 is 0
i.e. 4a - 2b = 15

Adding up the two equations and solving them gives us 
a = 5/4, and b = -5

Hence, a - b = 25/4


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