Condition of Common Roots

Problems on Condition For Common Roots

Problems on Condition For Common Roots

Problems based on Range of quadratic polynomial and Transformation of roots |Condition of common root | Range of quadratic polynomial

Condition of common root, Introduction to identity and its problem solving and Range of quadratic polynomial

Questions on identiity || Condition OF common root

What are the Condition for 1 Common root or both common root?

Discussion OF Ex.-10.3||Condition for Common Points in two circle:-(1) 0 Point common||(2) 1 Point common||(3)2 Point common,proOF OF Theorems

Illustrations on Common Roots

Suppose two quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 have a common root alpha , then a_(1)alpha^(2)+b_(1)alpha+c_(1)=0 " " …..(1) and a_(2)alpha^(2)+b_(2)alpha+c_(2)=0 " " ……(2) Eliminating alpha using crose - multiplication method gives us the condition for a common root Solving two equations simultaneously, the common root can be obtained. Now, consider three quadratic equations, x^(2)-2r p_(r )x+r=0, r=1, 2, 3 given that each pair has exactly one root common. In the notations of above problem, (gamma)/(alpha) is equal to