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If A and G are respectively arithmetic and geometric mean between positive no. a and b ; then the quadratic equation having a,b as its roots is `x^2-2Ax+G^2=0`.

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Verified by Experts

we have,
`A=(a+b)/2` and `G=sqrt(ab)`
The equation having `a` and `b` as its roots is:
`x^2-x(a+b)+ab=0` or `x^2-2Ax+G^2=0`
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. Find the two numbers whose A.M. is 25 and GM is 20.

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  2. If A and G are respectively arithmetic and geometric mean between posi...

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  3. The sum of two numbers is 6 times their geometric mean, show that numb...

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  4. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respecti...

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  5. If AM and GM of two positive numbers a and b are 10 and 8 respectively...

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  6. If the fifth term of a G.P. is 2, then write the product of its 9 term...

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  7. If (p+q)^(th) and (p-q)^(th) terms of a G.P. re m and n respectively, ...

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  8. If (log)x a , a^(x//2) and (log)b x are in G.P., then write the value ...

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  9. If the sum of an infinite decreasing G.P. is 3 and the sum of the squa...

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  10. If p^(th), q^(th) and r^(th) terms of G.P. are x,y,x respectively then...

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  11. If A1 and A2 are two A.M.s between a and b and G1 and G2 are two G.M b...

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  12. If second, third and sixth terms of an A.P. are consecutive terms of a...

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  13. If A and G are respectively arithmetic and geometric mean between posi...

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  14. If n geometric means are inserted between two quantities ; then the pr...

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  15. If a=1+b+b^2+b^3+ to oo , then write b in terms of a given that abs(b)...

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  16. If in an infinite G.P., first term is equal to 10 times the sum of all...

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  17. If the first term of a G.P. a1, a2, a3, . . . is unity such that 4a2...

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  18. If a ,b ,c are in A.P. and x , y , z are in G.P., then show that x^(b...

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  19. The first three of four given numbers are in G.P. and their last three...

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  20. If S be the sum P the product and R be the sum of the reciprocals of n...

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