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Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x...

Let `Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2a^2, 3x^3+6a^2x, 3x^4+12a^2x^2+2a^4]|` then

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" If " f(x) = |{:(3,,3x,,3x^(2)+2a^(2)),(3x,,3x^(2)+2a^(2),,3x^(3)+6a^(2)x),(3x^(2)+2a^(2),,3x^(3)+6a^(2)x,,3x^(4)+12a^(2)x^(2)+2a^(4)):}| then

Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3], [6x^2-x-2, 6x^2-7x+2, 12x^2-5x-2]|=0.

Factorise : 3x^5 - 6x^4 - 2x^3 + 4x^2 + x-2

Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

Add : 3x^(2)+5x-4, 2x+3-x^(2) and 8-3x+7x^(2) .

Divide 2x^5 -3x^4 +5x^3 -7x^2 +3x -4 by x-2.

Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]| =0.

Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

|[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]| =0

Simplify: 2x^2(x^3-x)-3x(x^4+2x)-2(x^4-3x^2)

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

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  2. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

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  3. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

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  4. Consider a system of linear equation in three variables x,y,z a1x+b...

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  5. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of det...

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  6. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degr...

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  7. If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]...

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  8. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

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  9. Let f(n)=|nn+1n+2^n Pn^(n+1)P(n+1)^n Pn^n Cn^(n+1)C(n+1)^(n+2)C(n+2)| ...

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  10. If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]...

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  11. Let x<1, then value of |[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]| is...

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  12. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

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  13. Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...

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  14. If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...

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  15. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  16. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  17. Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , where ai ' s are real and f(x)=...

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  18. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  19. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent o...

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

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