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If a ,\ b ,\ c are the roots of the eq...

If `a ,\ b ,\ c` are the roots of the equation `x^3+p x+q=0` , then find the value of the determinant `|(1+a,1 ,1), (1, 1+b,1),( 1, 1 ,1+c)|` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Show that: |[b+c,c+a ,a+b],[ q+r, r+p, p+q],[ y+z ,z+x,x+y]|=2|[a, b, ...

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  2. Prove that: determinant \begin{vmatrix} 1+ a & 1 & 1 \\ 1 & 1+b...

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  3. If a ,\ b ,\ c are the roots of the equation x^3+p x+q=0 , then find...

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  4. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

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  5. Show that: |(b+c)^2b a c a a b(c+a)^2c b a c b c(a+b)^2|=2a b c(a+b+c)...

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  6. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^...

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  7. Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c...

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  8. Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2...

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  9. Without expanding the determinant, show that (a+b+c) is a factor of ...

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  10. If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that d...

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  11. Find dy/dx if y=cos^2x

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  12. If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ ...

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  13. If a , b , c are real numbers, prove that \begin{vmatrix} a & b & ...

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  14. 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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  15. Using properties of determinants. Prove that |[3a,-a+b,-a+c], [-b+a,3b...

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  16. Using properties of determinants, solve for x:|[a+x, a-x, a-x], [a-x...

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  17. Using properties of determinants, solve the following for x: |[x-2,...

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  18. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  19. If a , b , c are all positive and are p t h ,q th and r t h terms of a...

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  20. If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c...

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