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If the sum of the roots of the quadratic equaion `ax^2+ bx +c =0` is equal to the sum of the squares of their reciprocals then prove that `a/c,b/a and c/b " are in HP "`

A

A.P.

B

G.P.

C

H.P.

D

None of these

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
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  4. if p,q,r are real numbers satisfying the condition p + q +r =0 , then ...

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  7. The set of all values of ' a ' for which the quadratic equation 3x^2+2...

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  8. Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,the...

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  9. If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2...

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  14. If alpha in (0,pi/2),t h e nsqrt(x^2+x)+(tan^2alpha)/(sqrt(x^2+x)) is ...

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  15. If a,b are real, then the roots of the quadratic equation (a-b)x^(2)-5...

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  16. If alpha, beta are the roots of the equation ax^(2) -bx +c=0 then eq...

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

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