Location of Roots
Location of Roots: Overview
This topic covers concepts, such as Quadratic Equation with Both the Roots Less than 'k', Quadratic Equation with Both the Roots Greater than 'k', Quadratic Equation with 'k' Lying between the Roots, etc.
Important Questions on Location of Roots
For how many integral values of , the equation , where is an integer has real roots and both of them lie in the interval ?

If are zeros of where for all , then the complete set of values of is

Let and be such that , then the quadratic equation has

The value of for which the quadratic expression is positive for exactly three integral values of is

If the quadratic equation has two distinct roots in where and then the minimum value of is

The values of for which each root of the equation is greater than , always satisfy the inequality

Given and . Then lies in the interval:

The values of for which the roots of the equation are real and exceed are -

For the given equation , what are the values of so that it contains two distinct real roots in the interval

The range of for which the equation has its smaller root in the interval is

Let the values of for which one root of the equation is smaller than and the other greater than be . Find


If lies between both the roots of , then


If the roots of the quadratic equation lie on either side of unity, then the number of integral values of is

The values of for which may have one root less than and other root greater than is

If has unique root in then length of largest continuous interval of in is

If and are the roots of the equation where are the eccentricities of an ellipse and hyperbola respectively then the value of belongs to

If roots of equation lie on either sides of unity, then number of integral values of is

Let If the equation has exactly one root in then number of possible integral values of is
