# Interval in which the Roots LieIn some problems we want the roots of the equation ax2 + bx + c = 0 to lie in a given interval. For this we impose conditions on a, b, and c. Let f(x) = ax2 + bx + c.(i)     If both the roots are positive i.e. they lie in (0, ¥), then the sum of the roots as well as the product of the roots must be positive.        Þa + b = – > 0 and ab =  > 0 with b2 – 4ac > 0.        Similarly, if both the roots are negative i.e. they lie in (–¥, 0) then the sum of the roots will be negative and the product of the roots must be positive.        i.e. a + b =   > 0 with b2 – 4ac > 0. In this why have we not used greater than equalto function for product of roots

Vikas TU
14149 Points
7 years ago
It is already strictly mentioned that the roots are both positive or negative.
for products of roots then if u are multiplying the roots having both positive or both negative will give a non-zero result alwas.
For the case zero only occurs if one of the roots is zero whixh is a contradiction.
Hence.