Question

completar o quadro com as raízes das equações​

Answer 1

6x²-54=0

Δ=b²-4ac

Δ=0²-4.6.(-54)

Δ=1296

$x=\frac{-b+/-\sqrt{delta} }{2a} \\ \\ x=\frac{-(-0)+/-\sqrt{1296} }{2.6}\\ \\ x=\frac{0+/-36}{12} \\ \\ x'=\frac{0+36}{12}=\frac{36}{12} =3\\ \\ x''=\frac{0-36}{12} =\frac{-36}{12}=-3$

4x²-48x=0

Δ=(-48)²-4.4.0

Δ=2304

$x=\frac{-(48)+/-\sqrt{2304} }{2.4}\\ \\ x=\frac{-48+/-48}{8} \\ \\ x'=\frac{-48+48}{8} =\frac{0}{8} =0\\ \\ x''=\frac{-48-48}{8} =\frac{-96}{8} =-12$

36x²-9=0

Δ=0²-4.36.(-9)

Δ=1296

$x=\frac{0+/-\sqrt{1296} }{2.36}\\ \\ x=\frac{0+/-36}{72}\\ \\  x'=\frac{0+36}{72}= \frac{36}{72} (:36)= \frac{1}{2} \\ \\ x''=\frac{0-36}{72} =\frac{-36}{72} (:36)=-\frac{1}{2}$

-1/2x²+5x=0

Δ=5²-4.(-1/2).0

Δ=25

$x=\frac{-(5)+/-\sqrt{25} }{2.-(\frac{1}{2})}\\ \\ x=\frac{-5+/-5}{-1}\\\\ \\ x'=\frac{-5+5}{-1} =0\\ \\ x''=\frac{-5-5}{-1} =\frac{-10}{-1} =10$