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Show that A.M. of the roots of x^(2) - 2...

Show that A.M. of the roots of `x^(2) - 2ax + b^(2) = 0 ` is equal to the G.M. of the roots of the equation `x^(2) - 2b x + a^(2) = 0` and vice- versa.

A

`A gt G`

B

`A ne G`

C

`A = G`

D

none of these

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

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  2. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

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  3. Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to ...

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  4. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

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  5. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

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  6. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

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  7. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

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  8. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  9. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

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  10. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

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  11. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  12. Fill in the blanks If the quadratic equations x^2+a x+b=0a n dx^2+b x+...

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  13. Find the values of a for which the roots of the equation x^2+a^2=8x+6a...

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  14. If the sum of the roots of the equation (a+1)x^2=(2a+3)x+(3a+4)=0 is -...

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  15. If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciproca...

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  16. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

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  17. Solve |x^2+4x+3|+2x+5=0.

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  18. For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3...

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  19. If 2+sqrt(3)i is a root of the equation x^2+p x+1=0 , then write the v...

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  20. If tan alpha tan beta are the roots of the equation x^2 + px +q =0(p!...

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