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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
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  2. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

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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. Let f(x)=|1+sin^2x cos^2x4s in2xsin^2\ \ x1+cos^2x4s in2xsin^2xcos^...

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  5. The parameter on which the value of the determinant |[1,a...

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

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  7. Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r...

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  8. The values of θ lying between 0 and π/2 and satisfying the equation ...

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  9. If |(a, a, x,),(m, m, m),(b, x, b)|=0 then x may be equal to- a.a b. ...

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  10. If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2...

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  11. The value of the determinant |(alpha,beta,l),(alpha,x, n),(alpha,beta,...

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  12. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+...

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  13. If the system of equations x+y-3=0,\ (1+K)x+(2+K)y-8=0\ &\ x-(1+K)y+(2...

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  14. 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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  15. The values of lambda for which the system of euations x+y+z=6x+2y+3z=1...

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

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  17. Let p be the sum of all possible determinabnts of order 2 having 0,...

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  18. Find A for 2sinAcosA−cosA−2sinA+1=0 ;-

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

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  20. Statement I: If a ,\ \ b , c in R\ a n d a!=b!=c\ a n d\ x ,\ y ,\ z ...

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