When f(x) = ax^3 - 6x^2 + bx - 5 is divided by x - 1, the remainder is -5. When f(x) is divided by x + 2, the remainder is 53. Find the ordered pair (a,b).
+526 Its given that
\(f(x)= ax^3-6x^2+bx-5\)
When f(x) is divided by x-1 we get remainder
\(r=b-a+1\)
⇒\(b-a+1=-5\)
⇒\(a-b=6\) ...(1)
Now, when f(x) is divided by x+2 we get remainder
\(r' = -8a-2b-29\)
⇒\(-8a-2b-29=53\)
⇒\(-8a-2b=82\)
⇒\(-4a-b=41\) ...(2)
Subtracting eq (1) from (2)
\(-4a-b-a+b=41-6\)
\(-5a=35\)
∴ \(a=-7\)
From eq (1)
\(b=-13\)
Hence the ordered pair (a,b) is (-7,-13).
~Thank You :)
