Explicação passo a passo:

b)

x² + 12x + 35 = 0

coeficientes

a = 1

b = 12

c = 35

Δ = b² - 4ac

Δ = 12² - 4 (1) .( 35)

Δ = 144 - 140

Δ = 4

[tex]x=\dfrac{-b\pm\sqrt{\Delta} }{2a}\\ \\ \\ x=\dfrac{-12\pm\sqrt{4} }{2.(1)}=\dfrac{-12\pm2}{2}\\ \\ \\ x'=\dfrac{-12+2}{2}=-\dfrac{10}{2}=\boxed{-5}\\ \\ \\ x"=\dfrac{-12-2}{2}=-\dfrac{14}{2}=\boxed{-7}[/tex]

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c)

5x² - 31x + 6 = 0​

a = 5

b = -31

c = 6

Δ = b² - 4ac

Δ = ( -31 )² - 4.( 5 ).(6)

Δ = 961 -120

Δ = 841

[tex]x=\dfrac{-b\pm\sqrt{\Delta} }{2a}\\ \\ \\ x=\dfrac{-(-31)\pm\sqrt{841} }{2.(5)}=\dfrac{31\pm29}{10}\\ \\ \\ x'=\dfrac{31+29}{10}=\dfrac{60}{10}=\boxed{6}\\ \\ \\ x"=\dfrac{31-29}{10}=\dfrac{2}{10}=\boxed{\dfrac{1}{5}}[/tex]