Question

1- Determine os zeros ou raizes

a f(x)=x ao quadrado -16
b) f(x)=x ao quadrado+ 3x
c) f(x)=x ao quadrado +3x-10
d) f(x)=4x ao quadrado -4x +2



Porfavorrrr genteeeeeee

Answer 1

Explicação passo-a-passo:

a) $\sf f(x)=x^2-16$

$\sf x^2-16=0$

$\sf x^2=16$

$\sf x=\pm\sqrt{16}$

• $\sf \red{x'=4}$

• $\sf \red{x"=-4}$

As raízes são $\sf 4~e-4$

b) $\sf f(x)=x^2+3x$

$\sf x^2+3x=0$

$\sf x\cdot(x+3)=0$

• $\sf \red{x'=0}$

• $\sf x+3=0$

$\sf \red{x=-3}$

As raízes são $\sf 0~e-3$

c) $\sf f(x)=x^2+3x-10$

$\sf x^2+3x-10=0$

$\sf \Delta=3^2-4\cdot1\cdot(-10)$

$\sf \Delta=9+40$

$\sf \Delta=49$

$\sf x=\dfrac{-3\pm\sqrt{49}}{2\cdot1}=\dfrac{-3\pm7}{2}$

$\sf x'=\dfrac{-3+7}{2}~\Rightarrow~x'=\dfrac{4}{2}~\Rightarrow~\red{x'=2}$

$\sf x"=\dfrac{-3-7}{2}~\Rightarrow~x"=\dfrac{-10}{2}~\Rightarrow~\red{x"=-5}$

As raízes são $\sf 2~e-5$

d) $\sf f(x)=4x^2-4x+2$

$\sf 4x^2-4x+2=0$

$\sf \Delta=(-4)^2-4\cdot4\cdot2$

$\sf \Delta=16-32$

$\sf \Delta=-32$

Como $\sf \Delta < 0$, não há raízes reais

Answer 2

Explicação passo-a-passo:

a)

$\mathrm{f(x) = x^2 - 16}$

$\mathrm{x^2 - 16 = 0}$

$\mathrm{x^2 = 16}$

$\mathrm{x = \pm~\sqrt{16}}$

$\mathrm{x = \pm~4}$

$\blue{\mathrm{x' = 4 \: \: e \: \: x'' = - 4}}$

raízes 4 e - 4

b)

$\mathrm{f(x) = x^2 + 3x}$

$\mathrm{x^2 + 3x = 0}$

$\mathrm{x(x + 3) = 0}$

$\blue{\mathrm{ x' = 0}}$

$\mathrm{x + 3 = 0}$

$\blue{\mathrm{x' = - 3}}$

raízes 0 e - 3

c)

$\mathrm{f(x) = x^2 + 3x - 10}$

$\mathrm{x^2 + 3x - 10 = 0}$

coeficientes: a = 1, b = 3, c = - 10

$\mathrm{\Delta = b^2 - 4ac}$

$\mathrm{\Delta = 3^2 - 4*1*(-10)}$

$\mathrm{\Delta = 9 + 40}$

$\mathrm{\Delta = 49}$

$\mathrm{x = \dfrac{- b \pm \sqrt{\Delta}}{2a}}$

$\mathrm{x = \dfrac{- 3 \pm \sqrt{49}}{2*(1)}}$

$\mathrm{x = \dfrac{- 3 \pm 7}{2}}$

$\mathrm{ x' = \dfrac{- 3 + 7}{2} = \dfrac{4}{2} = \blue{2}}$

$\mathrm{ x'' = \dfrac{- 3 - 7}{2} = \dfrac{- 10}{2} = \blue{- 5}}$

raízes 2 e - 5

d)

$\mathrm{f(x) = 4x^2 - 4x + 2}$

$\mathrm{4x^2 - 4x + 2 = 0}$

coeficientes: a = 4, b = - 4, c = 2

$\mathrm{\Delta = b^2 - 4ac}$

$\mathrm{\Delta = (-4)^2 - 4*4*2}$

$\mathrm{\Delta = 16 - 32}$

$\mathrm{\Delta = - 16}$

Delta negativo = não há raízes reais