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  • If ax^2+ax^2+bx^2+x-6 has x+2 as a factor and leaves remainder 4 when divided by x-2, find a and b.

If ax^2+ax^2+bx^2+x-6 has x+2 as a factor and leaves remainder 4 when divided by x-2, find a and b.

Answers (1)

f(x) = ax^3 + ax^2+bx^2+x-6 $ has x+2 as a factor , so f(-2)=0 \\ $ f(-2)=a(-2)^3 + a(-2)^2+b(-2)^2-2-6 =0 \\ -8a +4a +4b - 8 =0 \Rightarrow b =a + 2 ...(i)\\ f(2) = 4 \\ a(2)^3 + a(2)^2+b(2)^2+2-6 =4 \\ 8a + 4a + 4b - 4 = 4 \\ 3a + b = 2 ...(ii) \\ \text{From equation (i) and equation (ii)} \\ a =0 , b=2

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Ravindra Pindel

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