Question

For any value of discriminant real roots always exist. True or false

Answer 1

Answer:

no it is false. when D is smaller than 0,,, no real roots exists

Answer 2

The statement that for any value of discriminant real roots always exist is False.

• Real roots only exist whenever the discriminant is non-negative. That is if D is the determinant then for existence of real roots D≥0 is the necessary and sufficient condition.
• If D<0 then the roots will be imaginary and they are complex conjugate of each other.
• Because for D<0, there is a negative sign in between the square root and this makes the whole value imaginary.
• But for the other case this is either strictly positive or 0 which causes no problem and makes the two roots real.