Question

Determine as raízes ( ou zeros) das funções:
a) f(x)= x² + 2x - 3
b) f(x)= -4x² + 4x - 1

Answer 1

a)

$f(x)=x^2+2x-3\\\\x^2+2x-3=0\\\\a=1\,\,\,\,\,\,\,\,\,\,b=2\,\,\,\,\,\,\,\,\,\,c=-3\\\\\triangle=b^2-4ac\\\triangle=(2)^2-4.(1).(-3)\\\triangle=4+12\\\triangle=16\\\\x= \dfrac{-b \frac{+}{-} \sqrt{\triangle} }{2a}\\\\\\x= \dfrac{-2 \frac{+}{-} \sqrt{16} }{2}\\\\\\x= \dfrac{-2 \frac{+}{-}4 }{2}\\\\\\x'= \dfrac{2}{2}\\\\\\\boxed{x'=1}\\\\x"= -\dfrac{6}{2} \\\\\boxed{x"=-3}$

b)

$f(x)=-4x^2+4x-1\\\\-4x^2+4x-1=0\\\\a=-4\,\,\,\,\,\,\,\,\,\,b=4\,\,\,\,\,\,\,\,\,\,c=-1\\\\\triangle=b^2-4ac\\\triangle=(4)^2-4.(-4).(-1)\\\triangle=16-16\\\triangle=0\\\\x= \dfrac{-b \frac{+}{-} \sqrt{\triangle} }{2a}\\\\\\x= \dfrac{-4 \frac{+}{-} \sqrt{0} }{2.(-4)}\\\\\\x= \dfrac{-4}{-8}\\\\\\\boxed{x'=x"= \dfrac{1}{2}}$