If `f (x) = ax^2 + bx + c, a + b + c = 0` then one root is

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

If one of the roots of ax^(2) + bx + c = 0 is thrice that of the other root, then b can be

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

Suppose a, b, c in R, a ne 0. If a + |b| + 2c = 0 , then roots of ax^(2) + bx + c = 0 are

IF ax^2 + 2cx + b=0 and ax^2 + 2bx +c=0 ( b ne 0) have a common root , then b+c=

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) .

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) .

If the equations : 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 : 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 :