Question

Dada a função quadrática f(x)=-3x²+6x+9, calcule x para que f(x)=-15

Answer 1

$\mathrm{f(x)=-3x^2+6x+9}\\\\ \mathbf{*\ Para\ f(x)=-15:}\\\\ \mathrm{-15=-3x^2+6x+9\ \to\ 0=-3x^2+6x+9+15}\\ \mathrm{0=-3x^2+6x+24\ \to\ x^2-2x-8=0}\\\\ \mathbf{Aplicando\ a\ f\'ormula\ quadr\'atica:}\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-2)\pm\sqrt{(-2)^2-4.1.(-8)}}{2.1}=}\\\\ \mathrm{=\dfrac{2\pm\sqrt{4+32}}{2}=\dfrac{2+\sqrt{36}}{2}=\dfrac{2\pm6}{2}=1\pm3}\\\\ \mathrm{x=\{1+3,1-3\}\ \to\ \boxed{\mathbf{x=\{4,-2\}}}}$