# Thread: find out the equation with the roots given

1. ## find out the equation with the roots given

i need to find out the equation, the roots are given:

-1+2√2 and -1-2√2
2 2

pls help

2. Originally Posted by Ilsa
i need to find out the equation, the roots are given:

-1+2√2 and -1-2√2
2 2

pls help
$\displaystyle [x - (\frac{-1+2\sqrt2}{2})] \times [x - (\frac{-1-2\sqrt2}{2})]$

3. you can also use this formula

x^2 - (sum of roots) x + (product of roots ) = 0

4. x^2 + x + C = 0

x = [-1 +- sqrt(1 - 4C)] / 2

Get my drift?

5. i am using the formula bu can't get the equation, pls help by giving complete steps ~ thankyou.

6. Originally Posted by Ilsa
i am using the formula bu can't get the equation
Where are you stuck in the multiplication process?

7. $\displaystyle x^2-(sum \ of\ roots)x+product \ of \ roots=0$
$\displaystyle \\ \alpha= \frac{-1+2\sqrt{2}}{2}\ \ \beta= \frac{-1-2\sqrt{2}}{2}$
$\displaystyle \alpha+ \beta= \frac{-1+2\sqrt{2}}{2}\ +\frac{-1-2\sqrt{2}}{2}\ = \frac{-1}{2}+\frac{2\sqrt{2}}{2}\ +\frac{-1}{2}-\frac{2\sqrt{2}}{2}$
$\displaystyle \alpha+ \beta=\frac{-2}{2} =\ -1$
$\displaystyle \\ \alpha \beta= \{ \frac{-1+2\sqrt{2}}{2}\ \} \{ \frac{-1-2\sqrt{2}}{2} \} \ = \{ \frac{1-2\sqrt{2}}{2}\ \} \{ \frac{1+2\sqrt{2}}{2} \}$
$\displaystyle \\ \alpha \beta=\frac {\{1^2-(2\sqrt{2})^2\}}{4} \ = \frac{(1-8)}{4}=\frac{-7}{4}$
$\displaystyle \\ x^2-(\alpha +\beta)x+\alpha. \beta=0$
$\displaystyle \\ x^2-(-1)x+\frac{-7}{4}=0$
$\displaystyle \\ 4x^2+4x-7=0$