Question

Calcule o valor de P na equação x² – 4x + P = 0 de modo que as raízes sejam reais e distinta

Answer 1

$\large\boxed{\begin{array}{l}\sf x^2-4x+P=0\\\sf \Delta=b^2-4ac\\\sf\Delta=(-4)^2-4\cdot1\cdot P\\\sf\Delta=16-4P\\\sf \Delta\geqslant0\implies ra\acute izes~reais~e~distintas\\\sf 16-4P\geqslant0\\\sf -4P\geqslant-16\cdot(-1)\\\sf 4P\leqslant16\\\sf P\leqslant\dfrac{16}{4}\\\sf P\leqslant4\end{array}}$