how can I find a quadratic polynomial that is divisible by (x-1) ,dividing it by (x +1) the remainder is 10 and dividing it by (x-2) the remainder is 5. Thanks. Tomorrow I have an exam and can ask a question like this.
hi there, consider the polynomial $\displaystyle f(x) = ax^2+bx+c $
From the information supplied $\displaystyle f(1)=0, f(-1)=10$ and $\displaystyle f(2)=5$ input this.
You now have
$\displaystyle 0 = a(1)^2+b(1)+c $
$\displaystyle 10 = a(-1)^2+b(-1)+c $
$\displaystyle 5 = a(2)^2+b(2)+c $
simplifying gives
$\displaystyle 0 = a+b+c $
$\displaystyle 10 = a-b+c $
$\displaystyle 5 = 4a+2b+c $
can you solve this system?