Question

determine o valor de p na equacao x²-(p+5) +36=0 para que as raizes sejam iguais

Answer 1

Para que as raízes sejam iguais o delta deve ser igual a 0, então :

$\sf \Delta = 0 \\\\ b^2-4\cdot a\cdot c = 0 \\\\ \left[-(p+5)\right]^2-4\cdot 1\cdot 36 = 0 \\\\\ (p+5)^2 = 4\cdot 36 \\\\ p+5 = \pm\sqrt{4\cdot 36} \\\\ p+5 = \pm 2\cdot 6 \\\\ p = -5 \pm +12 \\\\ p= - 5 +12 \to p = 7 \\\\ p=-5-12 \to p = -17 \\\\ \underline{\text{os valores poss{\'i}veis de p s{\~a}o }} :\\\\ \huge\boxed{\sf \begin{array}{I} \displaystyle \sf p = 7 \ \ ; \ \ \sf p = -17 \end{array} }\checkmark$