70.1k views
5 votes
Use vietas formula to find the sum and the product of the roots of the equation

Use vietas formula to find the sum and the product of the roots of the equation-example-1
User Azhidkov
by
3.5k points

1 Answer

5 votes

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

User Bhiefer
by
3.7k points