Question

use the discriminant to determine how many and what kind of solutions the quadratic equation x²-x=-1/4 has

Answer 1

$\bf x^2-x=-\cfrac{1}{4}\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4x^2-4x=-1}\implies 4x^2-4x+1=0$

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+1} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} \boxed{0}&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-4)^2-4(4)(1)\implies 16-16\implies \boxed{0}$