Common Roots
Common Roots: Overview
This topic covers concepts, such as, Condition for the Common Roots, Common Root of Two Quadratic Equations, Quadratic Equations with Both Roots Common & Quadratic Equations with Exactly One Common Root etc.
Important Questions on Common Roots
If the quadratic equations and have a common root, then for non-zero real value of the sign of the expression is

If the equation and have a common root , then the value of the expression is

Two quadratic equations and have a common root. If the remaining roots of the first and second equations are positive integers and are in the ration respectively, then the common root is

Two quadratic equations and have common roots. If the sum of the remaining roots of first and second equation is then the common root is

If is a common root of the equations and , then the value of is

If is a common factor of and , then the value of is:

The pair of equation and will have _____.

and are roots of the quadratic equation and and are roots of the quadratic equation . If there is only one common root of the above two equations, then the possible value of is:

One of the value of such that and have a common root, is

The parabolas and intersect each other at two distinct points. What is the abscissa of one of these points?

The equations and have a common root, then

If the equations and have a real common root then the value of is equal to

Let and where is a real number. What is the sum of all possible values of for which the equations and have a common root ?

If the equations and have a common root, show that it must be or .

The equations and have one common root and the equation has equal roots. Prove that .

If the equation and (where ) have a common root, then show that, either or .

If the quadratic equations and have a common root then find .

If the equations and have exactly one non-zero common root, then prove that the other roots of the equations satisfy .

If are the roots of the equation and are the roots of the equation evaluate in term of Hence, show that is the condition for the existence of a common root of the two equations.

If the quadratic equations and have a common root then find .
