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show that the condition that the roots...

show that the condition that the roots of ` x^3 + 3 px^2 + 3 qx +r=0` may be in
h.P is ` 2q^3=r (3 pq -r)`

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show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in A.P " is" 2p^3 -3pq +r=0

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

The condition that the roots of x^(3)+ 3px^(2) + 3qx + r = 0 may be in A.P is

The condition that the roots of x^(3) + 3px^(2) + 3qx + r = 0 may be in G.P is

The condition that the product of two of the roots x^3 +px^2 +qx +r=0 is -1 is

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in G.P p^3 r= q^3

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P 2p^3 =9r (pq-3r)

AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE -2.2 (SHORT ANSWER QUESTIONS)
  1. Solve 9x^3-15x^2+7x-1=0 , given that two of its roots are equal .

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  2. If the two roots of 4x^3 + 20 x^2 -23x + 6=0 are equal then find ...

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  3. Given that one root of 2x^3+3x^2-8x+3=0 is double of another root , f...

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  4. Solve x^3 -7x^2 + 36 =0 given one root being twice the other .

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  5. solve x^3 -9x^2 + 14x+ 24 =0 given that two of the roots are i...

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  6. show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r...

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  7. show that the condition that the roots of x^3 + px^2 + qx +r=0...

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  8. show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r...

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  9. Solve the following equation ,given that the root of each are in A.P ....

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  10. solve the equations 32x^3 - 48 x^2 + 22 x -3=0, the roots being ...

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  11. solve the equations x^3 -3x^2 - 6x +8=0 the roots being ...

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  12. Solve 18x^3+81x^2+121x+60=0 given that one roots is equal to half the ...

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  13. If the roots of x^(4) - 2x^(3) - 21x^(2) + 22x + 40 = 0 are in A.P. t...

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  14. Find the condition that x^3-px^2+qx-r=0 may have the roots in G.P .

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  15. Solve the equation 3x^3 -26 x^2 + 52 x-24 =0 the roots being ...

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  16. Solve the equation 15x^3 - 23x^2 + 9x -1=0

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  17. Solve the equation 6x^3 -11 x^2 +6x -1=0

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  18. find the multiple roots of 8x^3 + 20 x^2 + 6 x-9 =0

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  19. find the multiple roots of 12x^3 +40x^2 +39 x + 9=0

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