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If the quadratic equation 4x^(2) -2(a+c-1)x + ac-b (a gt b gt c) then: |
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Answer» Both roots are greater than a `2x(2x-a) -c(2x -a) + 2x-b=0` `f(x) = (2x-a)(2x-c) + (2x-b)=0` `f(a/2) = a-bf(c/2)=c-b` `f(a/2)f(c/2)=(a-b)(c-b) lt 0` `therefore (a GT b gt c)` So exactly one root lie in `(c/2, a/2)` |
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