TS EAMCET · Maths · Quadratic Equation
The remainder of \(n^4-2 n^3-n^2+2 n-26\) when divided by 24 , is
- A 20
- B 21
- C 22
- D 23
Answer & Solution
Correct Answer
(C) 22
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} f(n) & =n^4-2 n^3-n^2+2 n-26 \\ & =n^3(n-2)-n(n-2)-26 \\ & =(n-2)\left(n^3-n\right)-26 \\ & =(n-2) n\left(n^2-1\right)-26 \\ & =(n-2)(n-1) n(n+1)-26\end{aligned}\) \[ =24 k-48+22 \] \([\because\) product of four consecutive natural numbers is divisible by…
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