The equation formed by decreasing each root of `ax^(2)+bx+c=0` by 1 is`2x^(2)+8x+2=0` then

The equation formed by decreasing each root of ax^(2) + bx + c = 0 by 2 is x^(2) + 4x +3= 0 then

The equation formed by increasing each roots of 2x^(2) - 3x - 1 = 0 by 2 is

If the ratio of the roots of the equation ax^(2)+bx+c=0 is m: n then

If the difference between the corresponding roots of x^(2)+ax+b=0and x^(2)+bx+a=0 is same and a ne b, then

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 1,2,3 are the roots of the equation x^(3) + ax^(2) + bx + c=0 , then

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If one root is common is equations x^(2)-ax+b=0 and x^(2 ) +bx-a=0 , then :

The equations ax^(2) + bx+ c =0, x^(3) -2x^(2) +2x -1 =0 have tow roots common, then find the value of a+b.

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