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If A, G & H are respectively te A.M., G....

If A, G & H are respectively te A.M., G.M. & H.M. of three positive numbers a, b, & c then the equation whose roots are a, b & c is given by

A

`x^(3) - 3Ax^(2) + G^(3) (3x - 1) = 0`

B

`x^(3) - 3Ax^(2) + 3(G^(3)//H) x-G^(3) = 0`

C

`x^(3) + 3Ax^(2) + 3(G^(3)//H) x - G^(3) = 0`

D

`x^(3) - 3Ax^(2) - 3(G^(3)//H) x + G^(3) = 0`

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The correct Answer is:
B
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H.P and relation || Question on A.M,G.M & H.M.

ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
  1. If a,b,c,d are in H.P., then ab+bc+cd is equal to

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  2. If a(a), a (2), a (3),…., a(n) are in H.P. and f (k)=sum (r =1) ^(n) a...

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  3. If A, G & H are respectively te A.M., G.M. & H.M. of three positive nu...

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  4. In an H.P., T(p) = q (p + q), T(q) = p (p + q), then p and q are the r...

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  5. If four positive numbers a, b, c, d are in H.P. then which one of the ...

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  6. The A.M., G.M. and H.M. between two positive numbers a and b are equal...

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  7. The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...

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  8. If 2(y-a) is the harmonic mean between y-x and y-z then x-a, y—a and z...

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  9. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

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  10. If a(1), a(2), a(3) and h(1), h(2), h(3) are the A.M.'s and H.M.'s bet...

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  11. If H(1), H(2),…., H(n) be n harmonic means between a and b then (H(1) ...

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  12. If n is a root of the equation (1 - ab) x^(2) - (a^(2) + b^(2)) x - (1...

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  13. If (1)/(b+c) , (1)/(c+a) and (1)/(a+b) are in AP, then a^(2), b^(2) an...

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  14. If three numbers are in G.P., then the numbers obtained by adding the ...

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  15. If three numbers are in H.P., then the numbers obtained by subtracting...

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  16. If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...

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  17. If a, b, c, d be four numbers of which the first three are in AP and t...

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  18. If S(k) denotes the sum of first k terms of a G.P. Then, S(n),S(2n)-S(...

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  19. If x, y, z be in A.P., then x + (1)/(yz), y + (1)/(zx), z + (1)/(xy) a...

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  20. Let the positive numebrs a,b,c,d be in A.P. Then abc,abd,acd,bcd re (A...

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