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Interval in which the Roots Lie In some problems we want the roots of the equation ax 2 + bx + c = 0 to lie in a given interval. For this we impose conditions on a, b, and c. Let f(x) = ax 2 + 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 b 2 – 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 b 2 – 4ac > 0. In this why have we not used greater than equalto function for product of roots

 

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

Grade:11

1 Answers

Vikas TU
14149 Points
5 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.

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