Question

3- Resolva as equações do 2º grau a seguir:

c) x² +11 x – 26 = 0 b) x² - 20 x + 96 = 0

Answer 1

Δ = b² - 4 . a . c
x = (-b±√Δ)/2.a


x² + 11x - 26 = 0

a = 1, b= 11, c = -26

Δ = 11² - 4 . 1 . (-26)
Δ = 121 + 124
Δ = 225

x = (-11 ± 15)/2

x' = 2
x'' = -13

Solução { 2 e -13 }
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x² - 20 x + 96 = 0

a = 1, b  = -20, c = 06

Δ = (-20)² - 4 . 1 . 96
Δ = 400 - 384
Δ = 16

x = (20 ± 4 )/2

x' = 12
x'' = 8

Solução {12 e 8}

Forte abraço!

Answer 2

Vamos Lá:

$\boxed{\large\textbf{Equa\c{c}\~ao do 2\° grau}}$

Resolvendo por "Delta"

$b) \ \ x^2-20x+96 = 0 \\\\ \\\ \Delta = b^2-4ac \\\ \Delta = 400-4*1*96 \\\ \Delta = 400-384 \\\\ \boxed{\Delta = 16} \\\\ .------------------------. \\\\ x1 = \mathsf{\dfrac{-b+ \sqrt{\Delta} }{2*a}} \rightarrow \mathsf{\dfrac{20+ \sqrt{16} }{2*1}} \rightarrow \mathsf{\dfrac{20+ 4 }{2}} \rightarrow \boxed{12} \\\\\ \\\ x2 = \mathsf{\dfrac{-b- \sqrt{\Delta} }{2*a}} \rightarrow \mathsf{\dfrac{20- \sqrt{16} }{2}} \rightarrow \mathsf{\dfrac{20- 4 }{2}} \rightarrow \boxed{8}$
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$c) \ \ x^2+11x-26 = 0 \\\\ \\\ \Delta = b^2-4ac \\\ \Delta = 121-4*1*-26 \\\ \Delta = 121+104 \\\\ \boxed{\Delta = 225} \\\\ .------------------------.\\\\ x1 = \mathsf{\dfrac{-b+ \sqrt{\Delta} }{2*a}} \rightarrow \mathsf{\dfrac{-11+ \sqrt{225} }{2*1}} \rightarrow \mathsf{\dfrac{-11+ 15 }{2}} \rightarrow \boxed{2} \\\\\ \\\ x2 = \mathsf{\dfrac{-b- \sqrt{\Delta} }{2*a}} \rightarrow \mathsf{\dfrac{-11- \sqrt{\225} }{2}} \rightarrow \mathsf{\dfrac{-11- 15 }{2}} \rightarrow \boxed{-13}$

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Resolvendo por "Soma e Produto"

$b) \ \ \mathsf{x^2-20x +96 = 0} \\\\ S = -b/a \\\\ P = c/a$

$S = 20/1 = 20 \\\\ P = 96/1 = 96$

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$\boxed{x1 = 12} \\\\ \boxed{x2 = 8}$
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Prova:

x1+x2 = ?
12+8 = 20
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x1*x2 = ?
18*8 = 96

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$c) \ \ \mathsf{x^2+11x -26 = 0} \\\\ S = -b/a \\\\ P = c/a$

$S = -11/1 = -11 \\\\ P = -26/1 = -26$

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$\boxed{x1 = -13} \\\\ \boxed{x2 = 2}$
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Prova:

x1+x2 = ?
-13+2 = -11 
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x1*x2 = ?
-13*2 = -26

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Resposta Final.    $\mathsf{b) \ \ S = \{ 8 , 12\}} \\\\ \mathsf{c) \ \ S = \{ -13 , 2\}}$

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Bons Estudos!!!
^^