Question

Qual o produto das raízes da equação x² - 9x + 20 = 0 ?
20
4
9
10

Answer 1

$\begin{array}{l}\sf x^2-9x+20=0\\\sf a=1\quad b=-9\quad c=20\\\sf x'\cdot x''=\left(\dfrac{ -b+\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}\right)\cdot\left(\dfrac{-b-\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}\right)\\\\\sf x'\cdot x''=\left(\dfrac{-(-9)+\sqrt{(-9)^2-4\cdot1\cdot20}}{2\cdot1}\right)\cdot\left(\dfrac{-(-9)-\sqrt{(-9)^2-4\cdot1\cdot20}}{2\cdot 1}\right)\\\\\sf x'\cdot x''=\left(\dfrac{9+\sqrt{81- 80}}{2}\right)\cdot \left(\dfrac{9-\sqrt{81-80}}{2}\right)\\\\\sf x'\cdot x''=\left(\dfrac{9+\sqrt1}{2}\right)\cdot\left(\dfrac{9-\sqrt1}{2}\right)\\\\\sf x'\cdot x''=\left(\dfrac{ 9+1}{2}\right)\cdot\left(\dfrac{9-1}{2}\right)\\\\\sf x'\cdot x''=\left(\dfrac{10}{2}\right)\cdot\left(\dfrac{8}{2}\right)~\therefore~ x'\cdot x''= 20\\\huge\boxed{ \boxed{ \boxed{ \boxed{ \sf \dagger \maltese~alternativa~A}}}}\end{array}$