If `[{:(2alpha+1," "3beta),(0,beta^(2)-5beta):}]=[{:(beta+3,beta^(2)+2),(0,-6):}]`
find the equation whose roots are alpha and beta.

Explanation

the given matrices wil be equal, iff
`2alpha+1=alpha+3impliesalpha=2`
`3beta=beta^(2)+2impliesbeta^(2)-3beta+2=0`
:. `beta=1,2 and beta^(2) -5beta=-6`
implies ` beta^(2) -5beta+6=0`
:. `beta=2,3`
from Eqs. (i) and (ii), we get `beta=2`
rArr `alpha=2, beta=2`
`therefore` "Required equation is `x^(2)-(2+2)x+2.2=0`
`x^(2) -4x+4=0`