a)
[tex]x {}^{2} - 5x - 14 = 0 \\ [/tex]
[tex]\boxed{a = 1 \: , \: b = - 5 \: , \: c = - 14} \\ [/tex]
[tex]S = - \frac{b}{a} = - \frac{ - 5}{1} = \frac{5}{1} = \boxed{5} \\ S = x _{1} + x _{2} = - 2 + 7 = \boxed{ 5} \\ [/tex]
[tex]P = \frac{c}{a} = \frac{ - 14}{1} = \boxed{ - 14} \\ P = x _{1} \: . \: x _{2} = - 2 \: . \: 7 = \boxed{ - 14} \\ [/tex]
[tex]\boxed{S = \left \{ - 2\: , \:7\right \}} \\ [/tex]
b)
[tex]x {}^{2} + 12x + 36 = 0 \\ [/tex]
[tex]\boxed{a = 1 \: , \: b = 12 \: , \: c = 36} \\ [/tex]
[tex]S = - \frac{b}{a} = - \frac{12}{1} = \boxed{ - 12} \\ S = x _{1} + x _{2} = - 6 + ( - 6) = - 6 - 6 = \boxed{ - 12} \\ [/tex]
[tex]P = \frac{c}{a} = \frac{36}{1} = \boxed{36} \\ P = x _{1} \: . \:x _{2} = - 6 \: . \: ( - 6) = 6 \: . \: 6 = \boxed{36} \\ [/tex]
[tex]\boxed{S = \left \{ - 6\right \}} \\ [/tex]
c)
[tex] - x {}^{2} - x + 42 = 0 \\ [/tex]
[tex]\boxed{a = - 1 \: ,\: b = - 1 \: , \: c = 42} \\ [/tex]
[tex]S = - \frac{b}{a} = - \frac{ - 1}{ - 1} = \boxed{ - 1} \\ S = x _{1} + x _{2} = - 7 + 6 = \boxed{ - 1} \\ [/tex]
[tex]P = \frac{c}{a} = \frac{42}{ - 1} = \boxed{ - 42} \\ P = x _{1} \: . \: x _{2} = - 7 \: . \: 6 = \boxed{ - 42} \\ [/tex]
[tex]\boxed{S = \left \{ - 7\: , \:6\right \}} \\ [/tex]
d)
[tex] - x {}^{2} - 2x + 48 = 0 \\ [/tex]
[tex]\boxed{a = - 1 \: , \: b = - 2 \: , \: c = 48} \\ [/tex]
[tex]S = - \frac{b}{a} = - \frac{ - 2}{ - 1} = \boxed{ - 2} \\ S = x _{1}+ x_{2} = - 8 + 6 = \boxed{ - 2} \\ [/tex]
[tex]P = \frac{c}{a} = \frac{48}{ - 1} = \boxed{ - 48} \\ P = x_{1} \: . \: x _{2} = - 8 \: . \: 6 = \boxed{ - 48} \\ [/tex]
[tex]\boxed{S = \left \{ - 8\: , \:6\right \}} \\ [/tex]
e)
[tex]3x {}^{2} - 9x + 6 = 0 \\ [/tex]
[tex]\boxed{a = 3 \: , \: b = - 9 \: , \: c = 6} \\ [/tex]
[tex]S = - \frac{b}{a} = - \frac{ - 9}{3} = \frac{9}{3} = \boxed{3} \\ S = x _{1} + x _{3} = 1 + 2 = \boxed{3} \\ [/tex]
[tex]P = \frac{c}{a} = \frac{6}{3} = \boxed{2} \\ P = x _{1} \: . \: x _{2} = 1 \: . \: 2 = \boxed{2} \\ [/tex]
[tex]\boxed{S = \left \{1\: , \:2\right \}} \\ [/tex]
Att. NLE Top Shotta
