Question

obtenha os zeros da função f dada por: a) f(x)=2x²-12 b) f(x)=-7x²+2x c) f(x)=x²+2x-15 d) f(x)=8x²-10x+3​

Answer 1

Explicação passo-a-passo:

a) f(x) = 2x² - 12

$2 {x}^{2} - 12 = 0 \\ 2 {x}^{2} = 12 \\ {x}^{2} = \frac{12}{2} \\ {x}^{2} = 6 \\ x = \sqrt{6}$

b) f(x) = -7x² + 2x

-7x² + 2x = 0

x (-7x + 2) = 0

-7x = -2

x1 = 2/7

x2 = 0

c) f(x) = x² + 2x - 15

${x }^{2} + 2x - 15 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x = \frac{ - 2 + - \sqrt{ {2}^{2} - 4 \times 1 \times ( - 15)} }{2 \times 2} \\ \\ x = \frac{ - 2 + - \sqrt{4 + 60} }{4} \\ \\ x = \frac{ - 2 + - \sqrt{64} }{4} \\ \\ x1 = \frac{ - 2 + 8}{4} = \frac{6}{4} = \frac{3}{2} \\ \\ x2 = \frac{ - 2 - 8}{4} = - \frac{ 10}{4} = - \frac{5}{2}$

d) f(x) = 8x² - 10x + 3

$8 {x}^{2} - 10x + 3 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x = \frac{ - ( - 10) + - \sqrt{ {( - 10)}^{2} - 4 \times 8 \times 3} }{2 \times 8} \\ \\ x = \frac{10 + - \sqrt{100 - 96} }{16} \\ \\ x = \frac{10 + - \sqrt{4} }{16} \\ \\ x1 = \frac{10 + 2}{16} = \frac{12}{16} = \frac{3}{4} \\ \\ x2 = \frac{10 - 2}{16} = \frac{8}{16} = \frac{1}{2}$