+9491 discriminant of first one = 162 - 4(4)(-9) = 400 ≠ 0
discriminant of second one = 802 - 4(2)(400) = 3200 ≠ 0
discriminant of third one = (-6)2 - 4(1)(-9) = 72 ≠ 0
discriminant of fourth one = (-12)2 - 4(4)(9) = 0
discrimimant of fifth one = (14)2 - 4(-1)(49) = 392 ≠ 0
The fourth one is the quadratic with one distinct root.
4x2 - 12x + 9 = 0 when
x = \(\frac{-(-12)\pm\sqrt{(-12)^2-4(4)(9)}}{2(4)}\ =\ \frac{12\pm0}{8}\ =\ \frac{12}{8}\ =\ \frac32\)
Here's a graph of all of them: https://www.desmos.com/calculator/vrjvowhts0
+9491 \(\begin{array}{} \phantom{=\qquad}\frac{\cos(90°+x)}{\cos(360°-x)\tan(180°-x)\cos(480°)}&\\~\\ =\qquad\frac{-\sin(x)}{\cos(360°-x)\tan(180°-x)\cos(480°)}&\qquad\text{because}\qquad \cos(90°+x)=-\sin (x) \\~\\ =\qquad\frac{-\sin(x)}{\cos(-x)\tan(180°-x)\cos(480°)}&\qquad\text{because}\qquad \cos(360°-x)=\cos(-x+360°)=\cos(-x) \\~\\ =\qquad\frac{-\sin(x)}{\cos(x)\tan(180°-x)\cos(480°)}&\qquad\text{because cos(x) is an even function,}\quad \cos(-x)=\cos(x) \\~\\ =\qquad\frac{-\sin(x)}{\cos(x)(-\tan(x))\cos(480°)}&\qquad\text{because}\qquad \tan(180°-x)=-\tan(x)\\~\\ =\qquad\frac{\sin(x)}{\cos(x)\tan(x)\cos(480°)}&\\~\\ =\qquad\frac{\sin(x)}{\cos(x)\tan(x)\cos(120°)}&\qquad\text{because}\qquad \cos(480°)=\cos(480°-360°)=\cos(120°) \end{array}\)
So far the only difference is because tan(180° - x) = -tan(x)
\(\begin{array}{} \phantom{=\qquad}\frac{\sin(x)}{\cos(x)\tan(x)\cos(120°)}&\\~\\ =\qquad\frac{\sin(x)}{\cos(x)}\cdot\frac{1}{\tan(x)\cos(120°)}&\\~\\ =\qquad\tan(x)\cdot\frac{1}{\tan(x)\cos(120°)}&\qquad\text{because}\qquad \frac{\sin(x)}{\cos(x)}=\tan(x)\\~\\ =\qquad\frac{1}{\cos(120°)}&\\~\\ =\qquad\frac{1}{(-\frac12)}&\qquad\text{because}\qquad \cos(120°)=-\frac12\\~\\ =\qquad-2& \end{array}\)
Check: https://www.wolframalpha.com/input/?i=cos(pi%2F2%2Bx)%2F(cos(2pi-x)tan(pi-x)cos(8pi%2F3))
