Question

Seja a função definida por h(x)=x^2-2x+3k. Sabendo que essa função tem uma única raíz, determine o valor real de k​

Answer 1

$\large\boxed{\begin{array}{l}\sf h(x)=x^2-2x+3k\\\sf para\,ter\,uma\,\acute unica\,ra\acute iz,\Delta\geqslant0.\\\sf\Delta=b^2-4ac\\\sf\Delta=(-2)^2-4\cdot1\cdot(3k)\\\sf\Delta=4-12k\\\sf4-12k\geqslant0\\\sf -12k\geqslant-4\cdot(-1)\\\sf12k\leqslant4\\\sf k\leqslant\dfrac{4\div4}{12\div4}\\\\\sf k\leqslant\dfrac{1}{3}\end{array}}$