Roots of quadratic equation are equal are real , if and only if   `b^2 - 4ac` = .....

Study the statement carefully. Statement I : Both the roots of the equation x^(2) - x + 1 = 0 are real. Statement II : The roots of the equations ax^(2) + bx + c = 0 are real if and only b^(2) - 4ac gt 0 . Which of the following options hold?

If roots of the quadratic equation bx^(2)-2ax+a=0 are real and distinct then

The roots of each of the following quadratic equation are real and equal , find k. (ii) kx(x-2)+6=0 .

If the roots of the quadratic equation x^(2) +2x+k =0 are real, then

If the roots of quadratic equation are equal , then the discriminant of the equation is "______"

Prove that the roots of the quadratic equation ax^(2)-3bx-4a=0 are real and distinct for all real a and b,where a!=b.

The quadratic equation ax^(2)+bx+c=0 has real roots if:

The roots of a pure quadratic equation exists only if "_______" .

If the roots of the quadratic equation x^(2)+6x+b=0 are real and distinct and they differ by atmost 4 then the least value of b is