Question

The roots of the equation x^2+4x+1=0 are alpha and beta. Without solving the equation

Answer 1

i. state the values of \[\alpha+ \beta and \alpha \beta\]

Answer 2

ii. find the value of\[\alpha^2+\beta^2\]

Answer 3

iii. find the equation whose roots are \[1 + 1 \div \alpha and 1+1 \div \beta\]

Answer 4

\[\alpha+\beta=-b/a=-4/1\]

Answer 5

\[\alpha \beta=c/a=1/1=1.\]

Answer 6

\[\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha \beta\] put the values

Answer 7

ok

Answer 8

how do i go about doing the third part

Answer 9

u put the roots as\[x^2-(\gamma+\delta)x+\gamma \delta=0\] where \[\delta and \gamma\] are the 3rd part's roots.

Answer 10

im a bit confused

Answer 11

what type of conf.

Answer 12

oh now i go about the third part that says find the equation because im trying to do it but not sure if its correct can i tell u the answer what i get when im finished