## Truman Group Title Find the quadratic equation whose solutions are: 2 + sqr(5) and 2 - sqr(5) I'm not just looking for an answer but rather to learn. 2 years ago 2 years ago

1. Truman

$2+ \sqrt{5} and 2 - \sqrt{5}$

2. amitlpu91

equation bcam x^2 - (a+b)x+ a.b =0 take a=2+sqr 5 , b=2-sqr -5

3. Truman

$x ^{2} - (a+b)x + ab = 0?$

4. Truman

this is from an example in my book, but I don't understand the example:

5. amitlpu91

tis what any quarratic equation can be form...

6. amitlpu91

if their two roots are given .got it ...now

7. Truman

|dw:1326657719757:dw|

8. Truman

that's the example from the book

9. amitlpu91

yea ........now plug in...

10. imperialist

If you are given 2 (or more than 2, it doesn't matter) roots of a polynomial, say a and b in this case, then that just means if you were to factor your polynomial, you would get $f(x)=(x-a)(x-b)$ By multiplying this together, you get the equation $x^2-(a+b)+ab$ Thus, in your example, you would just plug in $a=2+\sqrt{5}, b=2-\sqrt{5}$ to the above equation to reach your answer.

11. Truman

|dw:1326657923682:dw|

12. Truman

that's the books example typed out,

13. Truman

thank you, i'm trying it