STEP practice

When the polynomial f(x) is divided by (x – a)(x – b) theremainder is px + q. In the case b ≠ a, find p and q in termsof a, b, f(a) and f(b). In the case b = a, show that p = f’(a) andq = f(a) – af’(a).

I understand the part when b doesn't equal a. But for when they do equal the solution just states as a ->b, p = f'(a)
i found it a different way but dont know if its invalid

Please help

Reply 1

Noble.

17

Set up the divisibility statement with the polynomials.

You then want to evaluate it, and its derivative, at 'a' to find p and q.

Reply 2

zye

OP

This is what ive done
f(X)=px + q + g(X)(x-a)(x-b) so
f(a)=ap + q
f(b)=bp + q

so p= (f(a)-f(b))/a-b
Q= f(a) - a(p)

Then i did find the derivate at a which worked but the worked solution uses some limit as a goes to b and i dont understand it

Reply 3

Noble.

17

Original post by zye

This is what ive done
f(X)=px + q + g(X)(x-a)(x-b) so
f(a)=ap + q
f(b)=bp + q

so p= (f(a)-f(b))/a-b
Q= f(a) - a(p)

Then i did find the derivate at a which worked but the worked solution uses some limit as a goes to b and i dont understand it