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If alpha be a repeated root of a quadra...

If `alpha ` be a repeated root of a quadratic equation f(x) = 0 and A(x),B(x) , C(x) be polynomials of degree 3,4,5 respectively , then `F(x)=|(A(x),B(x),C(x)),(A(alpha),B(alpha),C(alpha)),(A^1(alpha),B^1(alpha),C^1(alpha))|`

A

not divisible by `(x-alpha)`

B

divisible by `(x -alpha)` , not by `(x -alpha)^2`

C

divisible by `(x-alpha)^2` , not by f(x)

D

divisible by f(x)

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
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  5. If y^2 =ax^2 + bx +c, then y^3(d^2y)/(dx^2) is

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  8. If f(x)=|(Sinx , 1, 0),(x - pi/2,Sinx,1),(0,1,Sinx)| then (df)/(dx) at...

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  9. If x = sint , y = cos pt , then

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  10. If f(x) = |(x,x^2,x^3),(1,2x,3x^2),(0,2,6x)|, then f^(1)(x)=

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  11. Let y = t^(10) +1 and x = t^8 +1 . Then (d^2y)/(dx^2) is

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  13. If y = ax^(n+1)+bx^(n+1) then x^2(d^2y)/(dx^2) is equal to

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  14. If x = phi (t), y = Psi(t) then (d^2y)/(dx^2) is

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  16. x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) ...

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  17. If x = e^(t)sint, y =e^(t)cost then (d^2y)/(dx^2) at t = pi is

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  18. If alpha be a repeated root of a quadratic equation f(x) = 0 and A(x)...

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  19. If y= ae^(nx)+be^(-nx),then (d^2y)/(dx^2)-n^2y is equal to

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  20. The nth derivative of the function f(x)=1/(1-x^2) [where x in (-1,1) ...

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