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Suppose A, B, C are defined as A = a^(2)...

Suppose A, B, C are defined as `A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2)`, and `C = a^(2)c + ac^(2) - b^(2)c - bc^(2)`, where `a gt b gt c gt 0` and the equation `Ax^(2) + Bx + C = 0` has equal roots, then a, b, c are in

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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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 2
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  3. Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), ...

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  6. If (a+b+c=0, find the nature of the roots of ttie equation (c^2-ab)x...

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  7. If a + b + c = 0 and a ne c then the roots of the equation (b + c - a)...

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  8. If the roots of the equation (x-b) (x-c) + (x-c) (x-a) + (x-a) (x-b)=0...

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  9. If the expression x^(2)-2 (Sigma a) x+3 Sigma ab=0 be a perfect square...

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  10. If a,b and c are real numbers then the roots of the equation (x-a)(x-b...

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  11. If three distinct positive numbers a, b, care in H.P.,then the equatio...

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  12. Find the condition if the roots of a x^2+2b x+c=0a n db x^2-2sqrt(a c ...

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  13. if a lt c lt b, then check the nature of roots of the equation (a ...

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  14. The value of m for which the equation x^(3)-mx^(2)+3x-2=0 has two root...

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  15. If a in Z and the equation (x-a) (x-10) +1=0 is integral roots, then t...

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  16. The equation (6-x)^(4)+(8-x)^(4)=16 has

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  17. If x^(2)+x+1 is a factor of ax^(3)+bx^(2)+cx+d, then the real root of ...

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  18. Let f(x) = ax^(3) + 5x^(2) - bx + 1. If f(x) when divide by 2x + 1 lea...

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  19. If x^3+3x^2-9x=c is of the form (x-alpha)^2(x-beta) , then c is equal ...

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  20. If the two roots of the euqation (lamda-1) (x^(2)+x+1)^(2)-(lamda+1)(x...

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