Suppose a, b, c are distinct real numbers. Let f(x)= | array lll x^ 3 +a^ 3 & x^ 2 -a^ 2…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Suppose a, b, c are distinct real numbers.
\[\operatorname{Let} f(x)=\left|\begin{array}{lll} x^{3}+a^{3} & x^{2}-a^{2} & x+a \\ x^{3}+b^{3} & x^{2}-b^{2} & x+b \\ x^{3}+c^{3} & x^{2}-c^{2} & x+c \end{array}\right|\]
Assertion : f (x) is a polynomial of degree 3 .
Reason : a, b, c are zeroes of f(x).
\[\operatorname{Let} f(x)=\left|\begin{array}{lll} x^{3}+a^{3} & x^{2}-a^{2} & x+a \\ x^{3}+b^{3} & x^{2}-b^{2} & x+b \\ x^{3}+c^{3} & x^{2}-c^{2} & x+c \end{array}\right|\]
Assertion : f (x) is a polynomial of degree 3 .
Reason : a, b, c are zeroes of f(x).
- If both assertion and reason are correct and reason is the correct explanation of assertion.
- If both assertion and reason are true but reason is not the correct explanation of assertion.
- If assertion is true but reason is false.
- If assertion is false but reason is true.
Answer
(C) If assertion is true but reason is false.
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Assertion : f (x) = array lll (1+x)^ 1 & (1+x)^ 2 & (1+c)^ 3 (1+x)^ 3 & (1+x)^ 3 & (1+x)^ 3 (1+x)^ 4 & (1+x)^…
- Let A be a symmetric matrix such that A 5 = O and B = I + A + A 2 + A 3 + A 4 , then B is
- For what value of x, the matrix [ array ccc 3-x & 2 & 2 2 & 4-x & 1 -2 & -4 & -1-x array ] is singular.
- a, b, c are non-zero real numbers. Then | array lll c & a & ~b a & ~b & ~b ~b & ~b & a array | = 0, if
- If a 2 + b 2 + c 2 = –2 and f (x) = Then f (x) is a polynomial of degree :
- Let P _ 4 = [ array lll 0 & 1 & 0 0 & 0 & 1 1 & 0 & 0 array ], P _ 5 = [ array lll 0 & 0 & 1 1 & 0 & 0 0 & 1…
- If A and B are square matrices of equal degree, then which one is correct among the following ?
- | array ccc 1 & a & a^ 2 (z-z) & z & (z-z) (z-z) & z & (z-z) array | depends on
More Matrices and Determinants questions · Browse all practice questions