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Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C...

Let `A=[[3x^2], [1], [6x]],B=[a,b,c]`and `C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2x,(x+2)^2],[ 2x,(x+2)^2, 5x^2]]` be three given matrices, where `a ,b ,ca n dx in Rdot` Given that tr(AB)=tr(C). If `f(x)=a x^2+b x+c ,` then the value of `f(1)` is ______.

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Knowledge Check

  • Let A= [{:(,3x^(2)),(,1),(,6x):}], B=[a,b,c] and C=[{:(,(x+2)^(2),5x^(2),2x),(,5x^(2),2x,(x+1)^(2)),(,2x,(x+2)^(2),5x^(2))]:} where, a,b c and x in R , Given that tr (AB)=tr(C ). Then the value of (a+b+c)

    A
    7
    B
    2
    C
    1
    D
    4

  • If a,b,c are in A.P.and f(x)= |(x+a,x^2+1,1),(x+b, 2x^2-1,1),(x+c,3x^2-2 , 1)| , then f'(x) is :

    A
    0
    B
    1
    C
    a+bc
    D
    `(abc)/(a+b+c)`

  • If f(x)=|(x+a^2,x^4+1,3),(x+b^2,2x^4+2,3),(x+c^2,3x^4+7,3)| where x ne 0 and f' (x) = 0 then a^2,b^2,c^2 are in

    A
    A.P.
    B
    G.P.
    C
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