Question

determine as raizes das funções quadrática:
a) y = x2 - 16
b) y=x2-4x
c) y=x2-13x+40
d) y=4x2 - 8x +5
30 pontos

Answer 1

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$\tt a)~\sf y=x^2-16\\\sf x^2-16=0\\\sf x^2=16\\\sf x=\pm\sqrt{16}\\\sf x=\pm4\checkmark \implies A(-4,0)~B(4,0)$

$\tt b)~\sf y=x^2-2x\\\sf x^2-2x=0\\\sf x\cdot(x-2)=0\\\sf x=0\\\sf x-2=0\\\sf x=2\\\sf A(0,0)~B(2,0)\checkmark$

$\tt c)~\sf y=x^2-13x+40\\\sf x^2-13x+40=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-13)^2-4\cdot1\cdot40\\\sf\Delta=169-160\\\sf\Delta=9\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-13)\pm\sqrt{9}}{2\cdot1}\\\sf x=\dfrac{13\pm3}{2}\begin{cases}\sf x_1=\dfrac{13+3}{2}=\dfrac{16}{2}=8\\\sf x_2=\dfrac{13-3}{2}=\dfrac{10}{2}=5\end{cases}\\\sf A(5,0)~B(8,0)\checkmark$

$\tt d)~\sf y=4x^2-8x+5\\\sf 4x^2-8x+5=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-8)^2-4\cdot4\cdot5\\\sf\Delta=16-80\\\sf\Delta=-64<0\implies \not\exists ~~x\in\mathbb{R}$