JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(a-2 b+c=1\) If \(f(x)=\left|\begin{array}{lll}{x+a} & {x+2} & {x+1} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right|,\) then
- A \(f(-50)=501\)
- B \(f(-50)=-1\)
- C \(f(50)=1\)
- D \(f(50)=501\)
Answer & Solution
Correct Answer
(C) \(f(50)=1\)
Step-by-step Solution
Detailed explanation
\(\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}+\mathrm{R}_{3}-2 \mathrm{R}_{2}\) \(f(x)=\left|\begin{array}{ccc}{a+c-2 b} & {0} & {0} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right|\) \(=(a+c-2 b)\left((x+3)^{2}-(x+2)(x+4)\right)\) \(=x^{2}+6 x+9-x^{2}-6 x-8=1\)…
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