જો દરેક \(i\, = 1, 2, 3,\) માટે \( p_i(x)\) એ \(x\) માં દ્રીઘાત બહુપદી છે અને \( p'_i(x)\) અને \(p"_i(x)\) એ પ્રથમ અને દ્રીતીય \(p_i(x)\) ના વિકલન છે કે જ્યાં \(A\left( x \right)=\left[ \begin{matrix}
{{p}_{1}}\left( x \right) & p_{1}^{'}\left( x \right) & p_{1}^{''}\left( x \right) \\
{{p}_{2}}\left( x \right) & p_{2}^{'}\left( x \right) & p_{2}^{''}\left( x \right) \\
{{p}_{3}}\left( x \right) & p_{3}^{'}\left( x \right) & p_{3}^{''}\left( x \right) \\
\end{matrix} \right]\) અને \(B(x)\,= [A(x)]^T\) \(A(x)\). તો \(|B(x)|\) મેળવો.

A \(x\) ની \(6\) ઘાત વાળી બહુપદી છે .
B \(x\) ની \(3\) ઘાત વાળી બહુપદી છે .
C \(x\) ની \(2\) ઘાત વાળી બહુપદી છે .
D \(x\) પર આધારિત નથી

Verified Solution

Answer & Solution

Correct Answer

(A) \(x\) ની \(6\) ઘાત વાળી બહુપદી છે .

Step-by-step Solution

Detailed explanation

It is clear from the above multiplication, the degree of determinant of \(B(x)\) can not be less than \(4\) . Let \({p_1}x = {a_1}{x^2} + {b_1}x + {c_1}\) \({p_2}x = {a_2}{x^2} + {b_2}x + {c_2}\) and \({p_3}x = {a_3}{x^2} + {b_3}x + {c_3}\) where…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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ચલ \(( x )\)	\(x _{1}\)	\(x _{1}\)	\(x _{3} \ldots \ldots x _{15}\)
આવૃતિ \((f)\)	\(f _{1}\)	\(f _{1}\)	\(f _{3} \ldots f _{15}\)