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Suppose the that quadratic equations ax^...

Suppose the that quadratic equations `ax^(2)+bx+c=0 and bx^(2)+cx+a=0` have a common root. Then show that `a^(3)+b^(3)+c^(3)=3abc`.

A

3

B

2

C

1

D

4

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A
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AAKASH SERIES-QUADRATIC EQUATIONS & EXPRESSIONS-PRACTICE EXERCISE
  1. If the equations x^(2)-ax+bc=0 and x^(2)+bx+ca=0 have a common root, t...

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  2. If the equation x^(2)+ax+b=0 and x^(2)+bx+a=0 have a common root, then...

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  3. Suppose the that quadratic equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0 h...

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  4. IF x^2 +bx +a=0, ax^2+x+b=0 have a common root and the first eq...

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  5. If the quadratic equation ax^(2) + 2cx + b = 0 and ax^(2) + 2x + c = 0...

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  6. the expression 2x ^2 + 4x +7 has minimum value m at x= alpha ...

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  7. The maximum value of the expression (x^(2)+x+1)/(2x^(2)-x+1), for x in...

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  8. A = The maximum value of 4x^(2) + 4x + 5 B = The maximum value of 8x...

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  9. The range of (x^(2)-x+1)/(x^(2)+x+1) is

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  10. Out of the two roots of x^(2)-2 lambda x + lambda^(2)-1= 0, one is gre...

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  11. Assertion (A): The roots of ax^(2) + bx + c = 0, where a != 0, b, c in...

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  12. If x in R, then the range of (x)/(x^(2)-5x + 9) is

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  13. If 4 lt x lt 8 then the value of 12x -x^(2) - 32 is

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  14. The greatest positive integral value of x for which 200 - x(10 + x) is...

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  15. The range of values of x which satisfy 2x^(2) + 9x + 4 lt 0 and x^(2) ...

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  16. If x^(2) + 6x-27 gt 0, -x^(2) + 3x + 4 lt 0, then x lies in the interv...

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  17. If 4x^(2) + kx + 3 ge 0 for all real values of x then k lies in the in...

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  18. The greatest negative integer satisfying x^(2) - 4x - 77 lt 0 and x^(2...

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  19. IF the inequation sqrt(3x -8) lt -2 then

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  20. The range of values of x for which the inequality (x-1)/(4x+5) lt (x-3...

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