If \(kx^{2}+5x-\frac{5}{4}=0\) has equal roots, then \(b^2-4ac=0\). \(a=k\), \(b=5\) and \(c= - \frac{5}{4}\). \(b^2-4ac=0\) \(5^2 -4\times k \times - \frac{5}{4}=0 ...

Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots.

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