Sign of a quadratic expression for real values of the variable

For real values of x, the sign of the quadratic expression f(x) = ax² +bx+c is the same as that of 'a' except when the roots of the equation ax²+bx+c are real and distinct and x lies between them.


ax²+bx+c is greater than 0 for all x Є R iff a is greater than 0 and D is less than zero. (D is discriminant b²-ac), and

ax²+bx+c is lesser than 0 for all x Є R iff a is less than 0 and D is less than zero.