JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, a \in R\). Then the sum of which the squares of all the values of a for \(2 f^{\prime}(10)-f^{\prime}(5)+100=0\) is
- A \(117\)
- B \(106\)
- C \(125\)
- D \(136\)
Answer & Solution
Correct Answer
(C) \(125\)
Step-by-step Solution
Detailed explanation
\(f ( x )=\left|\begin{array}{ccc} a & -1 & 0 \\ ax & a & -1 \\ ax & ax & a \end{array}\right|\) \(f(x)=a\left|\begin{array}{ccc}1 & -1 & 0 \\ x & a & -1 \\ x^{2} & a x & a\end{array}\right|\) \(=a\left[1\left(a^{2}+a x\right)+1\left(a x+x^{2}\right)\right]\)…
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