Question

write a quadratic equation with the given roots: 1+√11i and 1-√11i

Answer 1

\(2\pm 2\sqrt{11i}=-b\pm \sqrt{b^2-4ac}\) if a = 1

so let b = -2 and solve for c.

Answer 2

i dont know about that man

Answer 3

i keep getting x^2+2x+13

Answer 4

look a the quadratic formula and work backwards.

Answer 5

i dont know how to work the formula backwards. i thought there was an alternative way

Answer 6

anyone here to help me :{

Answer 7

have you done other cases when the roots weren't a complex number?

Answer 8

no i dont think so

Answer 9

keep in mind the website right now is very lagged

Answer 10

im getting the answer x^2+2x+13

Answer 11

yeah i can tell lol its really bad

Answer 12

if you had a quadratic, could you obtain its roots?

Answer 13

idk :(

Answer 14

well..... have you done quadratic factoring at all?

Answer 15

yeah i got x^2+1x+1x+2. but i dont know what to do about the 11i squared

Answer 16

ok... well ... gimme one sec

Answer 17

ok

Answer 18

ok so i got the answer lol

Answer 19

\(\bf x=1+\sqrt{11}\ i\implies x-1-\sqrt{11}\ i=0\implies ({\color{blue}{ x-1-\sqrt{11}\ i}})=0\\ \quad \\

x=1-\sqrt{11}\ i\implies x-1+\sqrt{11}\ i=0\implies ({\color{blue}{ x-1+\sqrt{11}\ i}})=0\qquad thus\\ \quad \\


({\color{blue}{ x-1-\sqrt{11}\ i}})({\color{blue}{ x-1+\sqrt{11}\ i}})=0\\ \quad \\
({\color{blue}{ x-1-\sqrt{11}\ i}})({\color{blue}{ x-1+\sqrt{11}\ i}})=\textit{original polynomial}\\
-------------------------------\\
recall \implies {\color{blue}{ (a-b)(a+b) = a^2-b^2}}\qquad thus\\ \quad \\
(x-1-\sqrt{11}\ i)(x-1+\sqrt{11}\ i)=0\\ \quad \\
\implies [{\color{blue}{ (x-1)}}-(\sqrt{11}\ i)][{\color{blue}{ (x-1)}}+(\sqrt{11}\ i)]=0\\ \quad \\
\implies {\color{blue}{ (x-1)}}^2-(\sqrt{11}\ i)^2=0\)

Answer 20

again, it was just a math typo. thank you for your time

Answer 21

yw

Answer 22

\[if~ a~and~b~are~roots~of~an~equation,
then \left( x-a \right)\left( x-b \right)=0~is~the~required~equation.\]
\[\left\{ x-\left( 1+\sqrt{11}\iota \right) \right\}\left\{ x-\left( 1-\sqrt{11}\iota \right) \right\}=0\]
\[\left\{ \left( x-1 \right)-\sqrt{11}\iota \right\}\left\{ \left( x-1 \right)+\sqrt{11}\iota \right\}=0\]
solve it.