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If the roots of the equation a(b-c)x^2+b...

If the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal, show that `2//b=1//a+1//cdot`

A

`(1)/(a) +(1)/(c )`

B

`a+c`

C

`1//a+c`

D

`a+1//c`

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The correct Answer is:
A
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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 2
  1. The equation (b-c) x^(2)+ (c-a) x+(a-b)=0 has

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  2. If the roots of the equation (b-c) x^(2)+(c-a) x+(a-b) =0 be equal, ...

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  3. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

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  4. If a, b, c are in H.P., then the equation a(b-c) x^(2) + b(c-a)x+c(a-b...

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  5. 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 ,d are four consecutive terms of an increasing A.P., then t...

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  7. If a,b,c in Q, then roots of the equation (b+c-2a) x^(2)+(c+a-2b) x+(a...

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

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

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

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

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

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

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

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

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

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

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

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

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