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Let alpha be a repeated root of a qua...

Let `alpha` be a repeated root of a quadratic equation `f(x)=0a n dA(x),B(x),C(x)` be polynomials of degrees 3, 4, and 5, respectively, then show that `|A(x)B(x)C(x)A(alpha)B(alpha)C(alpha)A '(alpha)B '(alpha)C '(alpha)|` is divisible by `f(x)` , where prime `(')` denotes the derivatives.

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
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  2. Statement 1: If differentiable function f(x) satisfies the relation f(...

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  3. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  7. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

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  8. (d)/(dx)cos^(-1)sqrt(cosx),0ltxlt(pi)/(2) is equal to

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  9. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

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  19. The value of lim(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2...

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