Question Number 168229 by mathlove last updated on 06/Apr/22
Answered by mr W last updated on 06/Apr/22
$${x}=\mathrm{2}: \\ $$$${P}\left(\mathrm{0}\right)−{P}\left(\mathrm{0}\right)=\mathrm{4}{a}−\mathrm{2}{b}+\mathrm{12}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{2}{a}−{b}+\mathrm{6}=\mathrm{0} \\ $$$${x}=\mathrm{4}: \\ $$$${P}\left(\mathrm{2}\right)−{P}\left(−\mathrm{2}\right)=\mathrm{16}{a}−\mathrm{4}{b}+\mathrm{12} \\ $$$${x}=\mathrm{0}: \\ $$$${P}\left(−\mathrm{2}\right)−{P}\left(\mathrm{2}\right)=\mathrm{12} \\ $$$$\mathrm{16}{a}−\mathrm{4}{b}+\mathrm{12}=−\mathrm{12} \\ $$$$\Rightarrow\mathrm{4}{a}−{b}+\mathrm{6}=\mathrm{0} \\ $$$$\Rightarrow{a}=\mathrm{0},\:{b}=\mathrm{6} \\ $$$$\Rightarrow{a}+{b}=\mathrm{6} \\ $$