Question

2) Determine fórmula: as soluções das raízes a seguir, usando a) 2x²+x-1=0 b) 2x²+2x−24=0 x) 3x² - 4x - 2 = -3 d) x² + 5x-2=-8 2 ) Determine fórmula : as soluções das raízes a seguir , usando a ) 2x² + x - 1 = 0 b ) 2x² + 2x − 24 = 0 x ) 3x² - 4x - 2 = -3 d ) x² + 5x - 2 = -8​

Answer 1

Resposta:

2: A) 0.5, -1

B)  3, -4

C) -0.333... ,-1

D) -2, -3

Answer 2

$a) \\ 2x {}^{2} + x - 1 = 0 \\ 2x {}^{2} + 2x - x - 1 = 0 \\ 2x \: . \: (x + 1) - (x + 1) = 0 \\ (x + 1) \: . \: (2x - 1) = 0 \\ x + 1 = 0 \\ \boxed{\boxed{\boxed{x = - 1}}} \\ 2x - 1 = 0 \\ 2x = 1 \\ \boxed{\boxed{\boxed{x = \frac{1}{2} }}}$

$b) \\ 2x {}^{2} + 2x - 24 = 0 \\ x {}^{2} + x - 12 = 0 \\ x {}^{2} + 4x - 3x - 12 = 0 \\ x \: . \: (x + 4) - 3(x + 4) = 0 \\ (x + 4) \: . \: (x - 3) = 0 \\ x + 4 = 0 \\ \boxed{\boxed{\boxed{x = - 4}}} \\ x - 3 = 0 \\ \boxed{\boxed{\boxed{x = 3}}}$

$c) \\ 3x {}^{2} - 4x - 2 = - 3 \\ 3x {}^{2} - 4x - 2 + 3 = 0 \\ 3x {}^{2} - x - 3x + 1 = 0 \\ x \: . \: (3x - 1) - (3x - 1) = 0 \\ (3x - 1) \: . \: (x - 1) = 0 \\ 3x - 1 = 0 \\ 3x = 1 \\ \boxed{\boxed{\boxed{x = \frac{1}{3} }}} \\ x - 1 = 0 \\ \boxed{\boxed{\boxed{x = 1}}}$

$d) \\ x {}^{2} + 5x - 2 = 8 \\ x {}^{2} + 5x - 2 - 8 = 0 \\ x {}^{2} + 5x - 10 = 0 \\ \boxed{a = 1 \: ,\: b = 5 \: , \: c = - 10} \\ x = \frac{ - b ±\sqrt{b {}^{2} - 4ac} }{2a} \\ x = \frac{ - 5 ± \sqrt{5 {}^{2} - 4 \: . \: 1 \: . \: ( - 10) } }{2 \: . \: 1} \\ x = \frac{ - 5 ± \sqrt{25 + 40} }{2} \\ \boxed{\boxed{\boxed{x = \frac{ - 5 ± \sqrt{65} }{2} }}}$

att. yrz