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If f(x)=a+b x+c x^2 and alpha,beta,gamma...

If `f(x)=a+b x+c x^2 and alpha,beta,gamma` are the roots of the equation `x^3=1,t h e n \ |[a,b,c],[b,c,a],[c,a,b]|` is equal to

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. If [] denotes the greatest integer less than or equal to the real numb...

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  3. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

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  4. If x ,y \ a n d \ z are not all zero and connected by the equations ...

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  5. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

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  6. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

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  7. For what values of k , the following system of equations possesses a...

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  8. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

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  9. Solve for x by Cramers rule x+y+z=6, x-y+z=2 3x+2y-4z=-5

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  10. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

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  11. Find the value of a \ a n d \ b if the system of equation a^2x-b y=a...

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  12. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

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  13. f(x)=|[cosx,x,1],[2sinx,x^2,2x],[tanx,x,1]| . Then value of lim(x->0)(...

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  14. If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c...

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

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  16. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

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  17. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

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  18. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

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  19. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

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  20. Prove that the value of each the following determinants is zero: |a...

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