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Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi'(x) and pi''(x) be the first and second order derivatives of pi(x) respectively.

and B(x) = [A(x)]TA(x). Then determinant of B(x)
  • a)
    Does not depend on x
  • b)
    Is a polynomial of degree 6 in x
  • c)
    Is a polynomial of degree 3 in x
  • d)
    Is a polynomial of degree 2 in x
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi(x) and ...
Let Pi = ai x2 + bix + ci ai ≠ 0
bi, ci ∈ R

use (i) C2 →  C2 – x C

So |B| = |AT| |A| = |A|2 = constant independent from n
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Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi(x) and pi(x) be the first and second order derivatives of pi(x) respectively.and B(x) = [A(x)]TA(x). Then determinant of B(x)a)Does not depend on xb)Is a polynomial of degree 6 in xc)Is a polynomial of degree 3 in xd)Is a polynomial of degree 2 in xCorrect answer is option 'A'. Can you explain this answer?
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Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi(x) and pi(x) be the first and second order derivatives of pi(x) respectively.and B(x) = [A(x)]TA(x). Then determinant of B(x)a)Does not depend on xb)Is a polynomial of degree 6 in xc)Is a polynomial of degree 3 in xd)Is a polynomial of degree 2 in xCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi(x) and pi(x) be the first and second order derivatives of pi(x) respectively.and B(x) = [A(x)]TA(x). Then determinant of B(x)a)Does not depend on xb)Is a polynomial of degree 6 in xc)Is a polynomial of degree 3 in xd)Is a polynomial of degree 2 in xCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let for i = 1, 2, 3 pi(x) be a polynomial of degree 2 in x, pi(x) and pi(x) be the first and second order derivatives of pi(x) respectively.and B(x) = [A(x)]TA(x). Then determinant of B(x)a)Does not depend on xb)Is a polynomial of degree 6 in xc)Is a polynomial of degree 3 in xd)Is a polynomial of degree 2 in xCorrect answer is option 'A'. Can you explain this answer?.
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