Question

Use vietas formula to find the sum and the product of the roots of the equation

Answer 1

Step 1

Vieta's formula

`\begin{gathered} ax^2+bx+c=0 \\ x_1+x_2=-(b)/(a) \\ x_1\cdot x_2=(c)/(a) \end{gathered}`

Step 2

Let

`ax^2+bx+c=0=-z^2+z`

then

`\begin{gathered} a=-1 \\ b=1 \\ c=0 \end{gathered}`

Step 3

replace

`\begin{gathered} x_1+x_2=(-(1))/(-1) \\ z_1+z_2=1 \end{gathered}`

and

`\begin{gathered} z_1\cdot z_2=(0)/(-1) \\ z_1\cdot z_2=0 \end{gathered}`

so, the answers are 1 and 0