Question

determine as raízes ou zeros reais das funções
a) f (x) = 10x² - 11x + 1
b) f (x) = - 4x² + 20 x = 25
c) f (x) = 6 x 2 - 3x + 1
d) f (x) = - x² + 36
e) f (x) = 3x² - 7x
f) f (x)= 5x²​

Answer 1

Resposta:

a)

$f(x) = 10x {}^{2} - 11x + 1 \\ f(x) = 10(x {}^{2} - \frac{11}{10} \times ) + 1 \\ f(x) + x = 10(x {}^{2} - \frac{11}{10} x + \frac{121}{400} ) + 1 \\ \\ f(x) + 10 \times \frac{121}{400} = 10(x {}^{2} - \frac{11}{10} x + \frac{121}{400} ) + 1 \\ \\ f(x) + \frac{121}{40} = 10(x - \frac{11}{20} {)}^{2} + 1 \\ \\ f(x) = 10(x - \frac{11}{20} {)}^{2} + 1 - \frac{121}{40} \\ \\ f(x) = 10(x - \frac{11}{20} {)}^{2} - \frac{81}{40}$

c)

$f(x) = 6 \times 2 - 3x + 1 \\ 0 = 12 - 3x + 1 \\ 0 = 13 - 3x \\ 3x = 13 \\ x = \frac{13}{3}$

e)

$f(x) = 3 {x}^{2} - 7x \\ f(x) = 3x \times (x - \frac{7}{3} )$

f)

$f(x) = 5x {}^{2} \\ 0 = 5 {x}^{2} \\ 5 {x}^{2} = 0 \\ {x}^{2} = 0 \\ x = 0$