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Question

'af(k)<0' is the necessary and sufficient condition for a particular real number k to lie between the roots of a quadratic equation f(x)=0, where f(x)=ax2+bx+c. If f(k1)f(k2)<0, then exactly one of the roots will lie between k1 and k2.

If c(a+b+c)<0<a(a+b+c), then
  1. one root is less than 0, the other is greater than 1
  2. one root lies in (,0) and the other in (0,1)
  3. one root lies in (0,1) and the other in (1,)
  4. both the roots lie in (0,1)


Solution

The correct option is B one root lies in (,0) and the other in (0,1)
c(a+b+c)<0<a(a+b+c)
f(0)f(1)<0
So, one root lie between 0 and 1.
af(1)>0
So, 1 doesn't lie between the roots.

Hence, one root lies in (,0) and the other in (0,1).

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