Question

Dada a equação X^2+2x+(3-m)=0.
Determine m de modo que a equação admita uma raiz real.

Answer 1

$\large\boxed{\begin{array}{l}\sf A\,equac_{\!\!,}\tilde ao\,ax^2+bx+c=0\\\sf admite\,uma\,ra\acute iz\,real\,quando\\\sf \Delta=0~onde\,Delta=b^2-4ac\end{array}}$

$\Large\boxed{\begin{array}{l}\sf x^2+2x+3-m=0\,admitir\acute a\\\sf uma\,\acute unica\,ra\acute iz\,real\,quando\,\Delta=0.\\\sf\Delta=b^2-4ac\\\sf\Delta=2^2-4\cdot1\cdot(3-m)\\\sf\Delta=4-12+4m\\\sf\Delta=4m-8\\\sf ou\,seja\,\\\sf4m-8=0\\\sf 4m=8\\\sf m=\dfrac{8}{4}\\\\\sf m=2\end{array}}$