BITSAT 2024 Shift 1 Paper

To determine the nature of the roots of the equation x2+bx−c=0 (where b,c>0 ), we need to consider the sign of the product of the roots.
Key Points:
If the roots are of the same sign:
The product of the roots is positive.
If the roots are of opposite signs:
The product of the roots is negative.
Let's analyze the given equation x2+bx−c=0 :
The product of the roots for the quadratic equation ax2+bx+c=0 is given by ‌

c

a

.
For our equation:
The product of the roots is ‌

−c

1

=−c.
Since c>0, the product −c is negative.
Conclusion:
The roots of the equation x2+bx−c=0 must be of opposite signs, as the product of the roots is negative.