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(A) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given equation:

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$\frac{5}{4}$

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(A) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given equation: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.Here,$a = k$,$b = -2 \sqrt{5}$,and $c = 4$.Substituting these values into the discriminant formula:$(-2 \sqrt{5})^{2} - 4(k)(4) = 0$$(4 	imes 5) - 16k = 0$$20 - 16k = 0$$16k = 20$$k = \frac{20}{16} = \frac{5}{4}$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.

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