Question

1) Em cada um dos itens abaixo, ache todos os zeros da função P.

(a) P(x) = x2 + 2x -4      

(b) P(x) = x2 - 4x + 3    


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Answer 1

Explicação passo-a-passo:

a) $x^2+2x-4=0$

$\Delta=2^2-4\cdot1\cdot(-4)$

$\Delta=4+16$

$\Delta=20$

$x=\dfrac{-2\pm\sqrt{20}}{2\cdot1}=\dfrac{-2\pm2\sqrt{5}}{2}$

$x'=\dfrac{-2+2\sqrt{5}}{2}~\longrightarrow~x'=-1+\sqrt{5}$

$x"=\dfrac{-2-2\sqrt{5}}{2}~\longrightarrow~x"=-1-\sqrt{5}$

b) $x^2-4x+3=0$

$\Delta=(-4)^2-4\cdot1\cdot3$

$\Delta=16+12$

$\Delta=4$

$x=\dfrac{-(-4)\pm\sqrt{4}}{2\cdot1}=\dfrac{4\pm2}{2}$

$x'=\dfrac{4+2}{2}~\longrightarrow~x'=\dfrac{6}{2}~\longrightarrow~x'=3$

$x"=\dfrac{4-2}{2}~\longrightarrow~x"=\dfrac{2}{2}~\longrightarrow~x"=1$