kominis3q

2022-07-25

Find the number k such that the given equation has exactly one real solution ${x}^{2}-kx+64=0$

berouweek

Expert

The given equation is ${x}^{2}-kx+64=0$
To solve K, use the discriminant
Here a = 1, b = -K, c = 64
${b}^{2}-4ac=0\phantom{\rule{0ex}{0ex}}\left(-K{\right)}^{2}-4\chi 1\chi 64=0\phantom{\rule{0ex}{0ex}}\left(K{\right)}^{2}-256=0\phantom{\rule{0ex}{0ex}}\left(K{\right)}^{2}=256\phantom{\rule{0ex}{0ex}}K=\sqrt{256}=16$

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