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Show that , if p,q,r are rational , the ...

Show that , if p,q,r are rational , the roots of the equation `x^2-2px+p^2-q^2+2pr-r^2=0` are rational .

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FULL MARKS-THEORY OF EQUATIONS -Additional Questions Solved
  1. Show that , if p,q,r are rational , the roots of the equation x^2-2px+...

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  2. Construct a cubic equation with roots 2,3,4.

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  3. If alpha, beta and gamma are the cubic equation x^3-6x^2+11x-6=0. From...

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  4. If the roots of x^4+5x^3-30x^2-40x+64=0 are in G. P , then find the ro...

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  5. Determine the value of k such that the equation (2k-5)x^2-4x-15=0 and ...

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  6. If alpha, beta , gamma are the roots of the equation x^3+px^2+qx+r=0 ....

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  7. alpha , beta , gamma are the roots of the equation x^3+3x^2+2x+1=0 . F...

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  8. Find a polynomial equation of minimum degree with rational coefficient...

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  9. Find a polynomial equation of minimum degree with rational co - effici...

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  10. If the roots of equation x^3+px^2+qx+r=0 are in A.P then show that 2p...

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  11. Solve 27x^3+42x^2-28x-8=0 given that its roots are in geometric progre...

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  12. Solve the equation 15x^3-23x^2+9x-1=0 . Where roots are in H . P

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  13. If one root of x^3+2x^2+3x+k=0 is sum of the other two roots then find...

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  14. If sum of the roots of the equation x^3-3x^2-16x+k=0 is zero then find...

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  15. Find all zeros of the polynomial x^3-5x^2-9x-5=0 , If 2 + I is a root.

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  16. Solve (x-3)(x-6)(x-1)(x+2)+54=0

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  17. Solve the equation (x-4)(x-2)(x-1)(x+1)+8=0

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  18. Solve : 3^(2x+4)+1=2.3^(x+2)

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  19. Solve : 2^(2x)-2^(2x+3)+2^4=0

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  20. Solve (x-4)(x+2)(x+3)(x-3)+8=0

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  21. Solve : (x+y)^(2//3)+2(x-y)^(2//3)=3(x^2-y^2)^(1//3) and 3x-2y=13.

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