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The coefficient of the quadratic equatio...

The coefficient of the quadratic equation `a x^2+(a+d)x+(a+2d)=0` are consecutive terms of a positively valued, increasing arithmetic sequence. Then the least integral value of `d//a` such that the equation has real solutions is __________.

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RESONANCE ENGLISH-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. In a G.P. of real numbers, the sum of the first two terms is 7. The su...

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  2. In a potato race, a bucket is placed at the starting point, which is 7...

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  3. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  4. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

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  5. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  6. Three friends whose ages form a G.P. divide a certain sum of money in ...

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  7. The roots of the equation x ^(5) - 40 x ^(4) + ax ^(3) + bx ^(2) + cx ...

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  8. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

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  9. If a, b, c are in A.P. and if (b-c)x^(2)++(c-a)x+a-b=0and2(c+a)x^(2)+(...

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  10. Along a road lies an odd number of stones placed at intervals of 10 m....

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  11. a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=...

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  12. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

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  13. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  14. If n is any positive integer, then find the number whose square is und...

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  15. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6)...

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  16. If S (1), S (2) , S (3)……., S (2n) are the sums of infinite geometric ...

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  17. Find the nth terms and the sum to n term of the series : 1^(2)+(1^(2...

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  18. Let a (j) = (7)/(4) ((2)/(3)) ^( j -1), j in N. lf b (j) = a (j) ^(2...

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  19. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

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  20. As show in the figure , the five circles are tangent to one another co...

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