(b+c)x^(2)-(a+b+c)x+a=0

If the equation x^(2)+abx+c=0 and x^(2)+acx+b=0 have a common root.Show that the quadratic equation containing the other roots is a(b+c)x^(2)+(b+c)x-abc=0

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 then the roots of the equation (a+b+c)x^(2)-(b+2c)x+c=0 are

If b is the harmonic mean of a and c and alpha, beta are the roots of the equation a(b-c)x^(2) + b(c-a) x+ c(a-b)=0 , then

If b is the harmonic mean of a and c and alpha, beta are the roots of the equation a(b-c)x^(2) + b(c-a) x+ c(a-b)=0 , then

If alpha,beta are the roots of the equation ax^2 + bx+c=0 then the roots of the equation (a + b + c)x^2-(b + 2c)x+c=0 are (a) c (b) d-c (c) 2c (d) 0

If one of the roots of the equation (b-c)x^(2) + b(c-a)x + c( a-b) = 0 is 1, what is the second root ?