Square roots of roots!

Algebra Level 3

The roots of $x^2-4x+9=0$ are $\alpha^2$ and $\beta^2$ . Find the value of ${\alpha}+{\beta}$ to 3 significant figures.

1 solution

Julian Yu
Jul 2, 2018

By Vieta's Theorem, $\alpha^2+\beta^2=4$ and $\alpha\beta=81$ .

Let $S={\alpha}+{\beta}.$ We square both sides to get $S^2=\alpha^2+\beta^2+2{\alpha\beta}=4+2\sqrt{9}=10$ .

Hence $S=\sqrt{10}=3.16$ to 3 significant figures.

Interesting approach! You can perhaps put a link to the wiki explaining Vieta's Theorem for those who don't know

Syed Hamza Khalid - 2 years, 9 months ago