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Let two numbers have arithmetic mean 9 a...

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

A

`x^2 + 18x + 16 = 0`

B

`x^2 - 18 x + 16 =0`

C

`x^2 + 18 x - 16 =0`

D

`x^2 - 18 x - 16 =0`

Text Solution

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The correct Answer is:
C
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Statement 1: If the arithmetic mean of two numbers is 5/2 geometric mean of the numbers is 2, then the harmonic mean will be 8/5. Statement 2: For a group of positive numbers (GdotMdot)^2=(AdotMdot)(HdotMdot)dot

Statement I : If the arithmetic mean of two numbers is (5)/(2) , geometric mean of the numbers is 2, then the harmonic mean will be (8)/(5) . Statement II : For a group of positive numbers (G.M.)^(2) = (A.M.) xx (H.M.)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

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  2. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

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  3. Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...

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  4. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  5. Let a1 , a2 , a3,.... be terms of an A.P. if (a1 + a2 +....+ ap)/(a1 +...

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  6. If a1,a2,.....an are in H.P., then the expression a1a2 + a2a3 + ... + ...

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  7. If the sum of first n natural numbers is 1/5 times the sum of their sq...

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  8. log3 2 , log6 2 and log12 2 are in

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  9. If x be the AM and y,z be two GM's between two positive numbers, then ...

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  10. If In (a + c), In(c - a) , In(a - 2b + c) are in A.P., then

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  11. The sum of the numerical series 1/(sqrt3 + sqrt7) + 1/(sqrt7 + sqrt11)...

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  12. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

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  13. The series of natural number is divided into groups 1 , 2, 3, 4,.........

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  14. sum(i = 1)^n sum(j = 1)^i sum(k = 1)^j 1 is equal to

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  15. The sides of a right angle triangle from a G.P. the tangent of the sma...

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  16. If the first & the (2n + 1)th terms of an A.P. , a G.P & an H.P. of po...

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  17. If the arithmetic mean of two positive numbers a & b (a gt b) is twice...

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  18. If Sn denotes the sum to n terms of the series (1 le n le 9) 1 + 22 + ...

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  19. If a , b , c are in H.P. , then

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  20. Let S1 , S2,,,,, be squares such that for each n ge 1 the length of a ...

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