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Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , w...

Let `f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x ,` where `a_i ' s` are real and `f(x)=0` has a positive root `alpha_0dot` Then `f^(prime)(x)=0` has a positive root `alpha_1` such that `0

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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

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

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

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

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

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  7. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,...

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

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  9. If |b+c c+a a+b a+b b+c c+a c+a a+b b+c|=k|ab c c a b b c a| , then va...

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  10. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  11. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

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  12. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

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  13. Prove that the value of each the following determinants is zero: |[(a^...

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  14. The value of the determinant [(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

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  15. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

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  16. Prove that the value of each the following determinants is zero: |[l...

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  17. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  18. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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

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

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