Given that a, b and c are real numbers such that b^2=4 a c and a> ₀ . The maximal possible set D R on which the function f: D R given by f(x)= a x^3+(a+b) x^2+(b+c) x+c is defined, is

Step-by-step solution

Given function, gathered f(x)= a x^3+(a+b) x^2+(b+c) x+c = (a x^2+b x+c )(x+1) gathered The function f(x) will be define, if aligned & (a x^2+b x+c )(x+1)>0 & and & x+1>0 a>0 and b^2=4 a c & aligned So, D=x: x (-1, ) . and .x - b 2 a or D=R- - b 2 a (- ,-1] .