Question

Calcule a soma e o produto das raízes das equações.

x² - 10x + 24 = 0​

Answer 1

Resposta:

x² - 10x + 24 = 0  

Δ = (-10)² - 4.1.24  

Δ = 100 - 96  

Δ = 4

///////////////////////////    

x' = -(-10) + √4  / 2 . 1  

x' = 10 + 2 / 2  

x' = 12/2  

x' = 6

///////////////////////////    

x" = -(-10) - √4  / 2 . 1  

x" = 10 - 2 / 2  

x" = 8/2  

x" = 4

///////////////////////////  

x' + x" = 6 + 4  = 10    

x' . x" = 6 . 4  = 24

///////////////////////////  

S = 10 e P = 24

Explicação passo a passo:

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{x^2-10x+24=0 }$

$\mathsf{ a=1\quad b=-10\quad c=24}$

$\mathsf{ x'+x''=\dfrac{-b+\sqrt\Delta}{2\cdot a}+\dfrac{-b-\sqrt\Delta}{2\cdot a}}$

$\mathsf{x'+x''=\dfrac{-b+\sqrt\Delta-b-\sqrt\Delta}{2\cdot a} }$

$\mathsf{x'+x''=\dfrac{-2\cdot b}{2\cdot a}~~ \therefore ~~x'+x''=\dfrac{-b}{a}}$

$\boxed{\boxed{ \mathsf{x'+x''=\dfrac{-(-10)}{1}=10}} }$

$\mathsf{ x'\cdot x''=\left(\dfrac{-b+\sqrt\Delta}{2\cdot a}\right)\cdot \left(\dfrac{-b-\sqrt\Delta}{2\cdot a}\right)}$

$\mathsf{x'\cdot x''=\dfrac{(-b)^2-b\sqrt\Delta+b\sqrt\Delta-(\sqrt\Delta)^2}{(2\cdot a)^2} }$

$\mathsf{x'\cdot x''=\dfrac{b^2-\Delta}{4\cdot a^2} }$

$\mathsf{ x'\cdot x''= \dfrac{b^2-(b^2-4\cdot a\cdot c)}{4\cdot a^2}}$

$\mathsf{x'\cdot x''=\dfrac{b^2-b^2+4\cdot a\cdot c}{4\cdot a^2} }$

$\mathsf{ x'\cdot x''=\dfrac{4\cdot a\cdot c}{4\cdot a^2}~~\therefore~~ x'\cdot x''=\dfrac{c}{a}}$

$\boxed{\boxed{ \mathsf{x''\cdot x''=\dfrac{24}{1}=24}} }$