Question

Pleaseeeee help me !

Find the number of real number solutions for the equation.

x^2 - 18 = 0
A. cannot be determined
B. 0
C. 1
D. 2

Answer 1

`x^2 - 18 = 0\\\\x^2=18\\\\x=√(18) \vee x=-√(18)`

So D

Answer 2

`\bf x^2-18=0\implies x^2+0x-18=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+0}x\stackrel{\stackrel{c}{\downarrow }}{-18} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ 0^2-4(1)(-18)\implies 0+72\implies 72\qquad \stackrel{\qquad\uparrow }{positive}`