Question

de acordo com a função f(x)=-3x2-x+8, determine os valores de m e p de maneira que:

*f(m)=-2

*f(p)=4

Answer 1

$f (m)=-3. m^{2} -m +8=-2 \\ -3 m^{2} - m +8+2=0 \\ -3m^{2} -m+10=0 \\ \Delta=(-1)^{2} -4. (-3).10 \\ \Delta=1+120 \\ \Delta=121 \\ = \frac{1\pm \sqrt{121} }{2. (-3)} \\ \\ m= \frac{1\pm11}{-6} \\ \\ m^{'} = \frac{1+11}{-6} = \frac{12}{-6} =-2; m^{"} = \frac{1-11}{-6} = \frac{-10}{-6} = \frac{5}{3} ; \\ m=\large\boxed {-2; \frac{5}{3} }$ $f (p)=-3.p^{2} -p +8=4 \\ -3 p^{2} - p +8-4=0 \\ -3m^{2} -m+4=0 \\ \Delta=(-1)^{2} -4. (-3).4 \\ \Delta=1+48 \\ \Delta=49 \\ = \frac{1\pm \sqrt{49} }{2. (-3)} \\ \\ m= \frac{1\pm7}{-6} \\ \\ m^{'} = \frac{1-7}{-6} = \frac{-6}{-6} =1; m^{"} = \frac{1+7}{-6} = \frac{8}{-6} =- \frac{4}{3} ; \\ m=\large\boxed {1;- \frac{4}{3} }$