Grade 11Algebra
Interval in which the Roots Lie
In 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
