Nusret Balcı TMUA Paper 1 · Question 18

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Nusret Balcı TMUA Paper 1 · Q18

Paper 1Algebra

Let $f(x)$ and $g(x)$ be two polynomials with coefficients in $\mathbb R$ , defined as:

f(x)=x^2-8x+\alpha\qquad g(x)=-x^2+4x+\beta

When both $f(x)$ and $g(x)$ are divided by $x-k$ , the remainders are 5 and 7, respectively.

Given that $k\in\mathbb R$ , find the largest possible value for the quantity $\alpha-\beta$ .

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