The quadratic expression `ax^(2)+bx+c>0` `AA x in R` ,then

The quadratic expression ax ^(2)+bx+c gt 0 AA x in R, then :

Graph of quadratic expression y=ax^(2)+bx+c is given then

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

If the minimum value of the quadratic expression y =ax ^(2)+bx +c is negative attained at negative vlaue of x, then :

For which of the following graphs of the quadratic expression f(x)=ax^(2)+bx+c , the product of abc is negative

For which of the following graphs of the quadratic expression y=ax^(2)+bx+c , the product a.b.c is negative.

Statement-1: If x^(2) + ax + 4 gt 0 "for all" x in R , then a in (-4, 4) . Statement-2: The sign of quadratic expression ax^(2) + bx + c is always same as that of 'a' except for those values of x which lie between its roots.

The roots of a quadratic equation ax^(2) + bx + c=0 are 1 and c/a , then a + b = "_____" .

LET the equation ax^2+bx+c=0 has no real roots Assertion (A): c(a+b+c)gt0 , Reason (R): A quadratic expression ax^2+bx+c has signs same as that of al for all real x if the roots of the corresponding equation ax^2+bx+c=0 are imaginary. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.