Question

Alguém pode me ajuda preciso entregar amanhã

Answer 1

Fórmula para achar o delta (discriminante):

$\boxed{\Delta = b^2-4*a*c}$

Fórmula de Bháskara:

$\boxed{x = \frac{-b\pm\sqrt{\Delta}}{2a}}$

Estarei usando a fórmula de Bháskara direta, não irei enrolar muito nos cálculos pois é algo bastante simples.

A)

$x^2+5x+6=0 \Rightarrow \boxed{a = 1, b = 5, c = 6} \Downarrow \\ \Delta = 25 - 24 \\ \Delta = 1 \\\\ x' = \frac{-5+1}{2} = -\frac{4}{2} = \boxed{-2} \\ x'' = \frac{-5-1}{2} = -\frac{6}{2} = \boxed{-3}$

B)

$x^2-7x+12=0 \Rightarrow \boxed{a = 1, b = -7, c = 12} \Downarrow \\ \Delta = 49-48 \\ \Delta = 1 \\\\ x' = \frac{7+1}{2} = \frac{8}{2} = \boxed{4} \\ x'' = \frac{7-1}{2} = \frac{6}{2} = \boxed{3}$

C)

$x^2+5x+4=0 \Rightarrow \boxed{a = 1, b = 5, c = 4} \Downarrow \\ \Delta = 25 -16 \\ \Delta = 9 \\\\ x' = \frac{-5+3}{2} = -\frac{2}{2} = \boxed{-1} \\ x'' = \frac{-5-3}{2} = -\frac{8}{2} = \boxed{-4}$

D)

$7x^2+x+2=0 \Rightarrow \boxed{a = 7, b = 1, c = 2} \Downarrow \\ \Delta = 1-56 \\ \Delta =-55 \\\\ Para \ \Delta < 0 \ \boxed{x \notin \mathbb{R}}$

E)

$2x^2+5x-3=0 \Rightarrow \boxed{a = 2, b = 5, c = -3} \Downarrow \\ \Delta = 25 +24 \\ \Delta = 49 \\\\ x' = \frac{-5+7}{4} = \frac{2}{4} = \boxed{\frac{1}{2}} \\ x'' = \frac{-5-7}{4} = \frac{-12}{4} = \boxed{-3}$

F)

$6x^2+x-1=0 \Rightarrow \boxed{a = 6, b = 1, c = -1} \Downarrow \\ \Delta = 1 + 24 \\ \Delta = 25 \\\\ x' = \frac{-1+5}{12} = \frac{4}{12} = \boxed{\frac{1}{3}} \\ x'' = \frac{-1-5}{12} = \frac{-6}{12} = \boxed{-\frac{1}{2}}$

G)

$2x^2+3x+1=0 \Rightarrow \boxed{a = 2, b = 3, c = 1} \Downarrow \\ \Delta = 9-8 \\ \Delta = 1 \\\\ x' = \frac{-3+1}{4} = \frac{-2}{4} = \boxed{-\frac{1}{2}} \\ x'' = \frac{-3-1}{4} = \frac{-4}{4} = \boxed{-1}$

H)

$x^2-18x+45=0 \Rightarrow \boxed{a = 1, b = -18, c = 45} \Downarrow \\ \Delta = 324-180 \\ \Delta = 144 \\\\ x' = \frac{18+12}{2} = \frac{30}{2} = \boxed{15} \\ x'' = \frac{18-12}{2} = \frac{6}{2} = \boxed{3}$

I)

$x^2-6x+9=0 \Rightarrow \boxed{a = 1, b = -6, c = 9} \Downarrow \\ \Delta = 36 - 36 \\ \Delta = 0 \\\\ x' e\ x'' = \frac{6}{2} = \boxed{3}$

J)

$x^2-x-2=0 \Rightarrow \boxed{a = 1, b = -1, c = -2} \\ \Delta = 1 + 8 \\ \Delta = 9 \\\\ x' = \frac{1+3}{2} = \frac{4}{2} = \boxed{2} \\ x'' = \frac{1-3}{2} = \frac{-2}{2} = \boxed{-1}$