Answer
[tex] \green{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
1.)x²+5x+6=0
Roots: x = -2, x = -3
2.)x²-9x+14=0
Roots: x = 7, x = 2
3.)x²+4x-12
Roots: x = 2, x = -6
4.)x²-2x-15
Roots: x = 5, x = -3
5.)2x²-5x-12=0
Roots: x = 4, x = - 3/2
[tex] \green{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
Solution
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
[tex] \boxed{1.) \tt{x}^{2} + 5x + 6 = 0}[/tex]
[tex](x + 2)(x + 3) = 0 \\ \boxed{ x = - 2 | x = - 3}[/tex]
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
[tex] \boxed{ 2.)\tt{x}^{2} - 9x + 14 = 0}[/tex]
[tex](x - 7)(x - 2) = 0 \\ \boxed{x = 7 |x = 2 }[/tex]
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
[tex] \boxed{ \tt{3.) {x}^{2} + 4x - 12 }}[/tex]
[tex](x - 2)(x + 6) = 0 \\ \boxed{x = 2 | x = - 6}[/tex]
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
[tex] \boxed{ \tt{4.){x}^{2} - 2x - 15 = 0}}[/tex]
[tex](x - 5)(x + 3) = 0 \\ \boxed{x = 5 | x = - 3}[/tex]
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
[tex] \boxed{ \tt5.)2 {x}^{2} - 5x - 12}[/tex]
[tex] \tt{x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} } \\ [/tex]
[tex] \tt{x = \frac{ -( - 5)± \sqrt{ {( - 5)}^{2} - 4(2)( - 12) } }{2(2)} }[/tex]
[tex] \tt{x = \frac{5± \sqrt{25 + 96} }{4}} \\[/tex]
[tex] \tt{x = \frac{5± \sqrt{121} }{4}} \\ \\ \tt{x = \frac{5 + 11 }{4}}, \: x = \frac{5 - 11}{4} \\ \boxed{ \tt{x = 4 | - \frac{3}{2} }}[/tex]
[tex] \purple{﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌}[/tex]
