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Question

If a, b, c are in A.P, then the equation (ab)X2+(ca)X+(bc)=0 has two roots which are


  1. Real and unequal

  2. Real and equal

  3. Imaginary

  4. None of these


Solution

The correct option is B

Real and equal


If a,b,c are in A.P

b-a=c-b-------(1)
For the given quadratic equation, sum of coefficients = 0\)
1 is a root(You can verify this by substituting 1 in the given equation)\)
The other root, β is bcab[βX1=bcab]bc=ab(from(1))
β=1 or roots are real and equal

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