Question

Determine,se existirem, os zeros das funções quadráticas usando a fórmula :
d) f(x) = x² + 10x + 25
e) f(x) = x² - 8x + 16
f) f(x) = 25x² + 9x + 1

Answer 1

$d) f(x) = x^2 + 10x + 25\\\\ a=1;b=10;c=25\\\\ \Delta=b^2-4ac\to \Delta=10^2-4*1*25\to \Delta=100-100\to \Delta=0\\\\x' = x''\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-10\pm \sqrt{0} }{2*1} \to x= \frac{-10\pm 0 }{2} \to \\\\ x'=x''= \frac{-10 }{2} \to x'=x''=5\\\\\\ S=(5)$





$e) f(x) = x^2 - 8x + 16\\\\ a=1;b=-8;c=16\\\\ \Delta=b^2-4ac\to \Delta=(-8)^2-4*1*16\to \Delta=64-64\to \Delta=0\\\\ x' =x''\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-8)\pm \sqrt{0} }{2*1} \to x= \frac{8\pm 0 }{2} \to \\\\ x'=x''= \frac{8 }{2} \to x'=x''=4\\\\\\ S=(4)$





$f) f(x) = 25x^2 + 9x + 1\\\\ a=25;b=9;c=1\\\\ \Delta=b^2-4ac\to \Delta=9^2-4*25*1\to \Delta=81-100\to \Delta=-19$

Essa função não tem zero real, pois $\Delta\ \textless \ 0$




Espero ter ajudado...