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The determinant |a b aalpha+bb c balpha+...

The determinant `|a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0,` if `a ,b , c` are in A.P. `a ,b ,c` are in G.P. `a ,b ,c` are in H.P. `alpha` is a root of the equation `a x^2+b c+c=0` `(x-alpha)` is a factor of `a x^2+2b x+c`

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ALLEN-DETERMINANTS-All Questions
  1. If f^(prime)(x)=|m x m x-p m x+p nn+p n-p m x+2n m x+2n+p m x+2n-p| , ...

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  2. The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a ...

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  3. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  4. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  5. If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  6. If |a a x m m m b x b|=0,\ then x may be equal to- a.a b. b c.a+b d. ...

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  7. The value of the determinant |alphabetalalphax nalphabetax| is indepen...

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  8. If the determinant |a+p l+x u+fb+q x+y v+gc+r n+z w+h| splits into exa...

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  9. The values of lambda for which the system of euations x+y+z=6, x+2y+3z...

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  10. If x , y , z are in A.P. , then the value of the determinant are in A....

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  11. Statement 1 is True: Statement 2 is True; Statement 2 is a correct ...

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  12. Comprehension 2 Consider the system of linear equations alphax+y...

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  13. Comprehension 2 Consider the system of linear equations alphax+y...

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  14. Without expanding the determinant prove that: |0b-c-b0a c-a0|=0

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  15. Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

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  16. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

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  17. By using properties of determinants. Show that:|1+a^2-b^2 2a b-2b2a b1...

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  18. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  19. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

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  20. a+b+c=0, solve for x : [[a-x,c,b],[c,b-x,a],[b,a,c-x]]=0

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