Find the value(s) of k for which the given quadratic equations has real and distinct roots :
(i) `2x^(2)+kx+4=0` (ii) `4x^(2)-3kx+1=0`
(iii) `kx^(2)+6x+1=0` (iv) `x^(2)-kx+9=0`

Explanation

To find the values of \( k \) for which the given quadratic equations have real and distinct roots, we will use the discriminant \( D \) of a quadratic equation of the form \( ax^2 + bx + c = 0 \). The discriminant is given by:

\[ D = b^2 - 4ac \]

For the roots to be real and distinct, we need \( D > 0 \).

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