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If the quadratic has one real root, then \({b^2} - 4ac = 0\)

We have \(a = 1\), \(b = 2k\) and \(c = 36\).

\({b^2} - 4ac = 0\)

\({(2k)^2} - (4 \times 1 \times 36) = 0\)

\(4{k^2} - 144 = 0\)

\(4{k^2} = 144\)

\({k^2} = \frac{{144}}{4}\)

\({k^2} = 36\)

\(k = \sqrt {36}\)

\(k = \pm 6\)