For the equations `x^2+bx+c=0` and `2x^2+(b+1)x+c+1=0` select the correct alternative

If the equations ax^2 + bx + c = 0 and x^2 + x + 1= 0 has one common root then a : b : c is equal to

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then

If the equations ax^(2)+bx+c=0 and x^(2)+x+1=0 has one common root then a:b:c is equal to

If the equation : x^(2 ) + 2x +3=0 and ax^(2) +bx+ c=0 a,b,c in R have a common root then a: b: c is :

If the equation ax^(2)+2bx+c=0 and x^(2)+2p^(2)x+1=0 have one common root and a,b,c are in AP(p^(2)!=1), then the roots of the equation x^(2)+2p^(2)x+1=0 are

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .