Question

Dada a função quadrática f(x) = 4x²−11x −3 determine o valor de k sabendo-se que f(k) = f(k+1).

Answer 1

$\text{f(x)}=4\text x^2-11\text x-3 \\\\ \text{f(k) = f(k+1) } \ ; \ \text k = \ ? \\\\ \underline{\text{substituindo}}: \\\\ 4.\text k^2-11\text k -3=4(\text k+1)^2-11(\text k+1)-3 \\\\ 4\text k^2-11\text k = 4(\text k^2+2\text k+1)-11\text k-11 \\\\ 4\text k^2-11\text k =4\text k^2+8\text k+4-11\text k-11 \\\\ 8\text k +4-11=0 \\\\ 8\text k = 11-4 \\\\\ \huge\boxed{\text k = \frac{7}{8}\ }\checkmark$