If the roots of the equadratic equation `x^(2) + px + q = 0 " are " tan23^(@) "and" tan22^(@),` then find the value of q - p .

Explanation

`x^(2) + px + q` = 0 has roots `tan23^(@) and tan22^(@)`
`therefore tan 23^(@) + tan 22^(@) = -p` …(1)
and `tan 23^(@) tan22^(@)= q`
Now, `tan45^(@) = tan(23^(@) + 22^(@))` …(2)
`rArr 1 = (tan23^(@) + tan22^(@))/(1-tan23^(@)tan22^(@))`
`rArr 1 = (-p)/(1 - q)` [Using (1) and (2)]
`rArr 1 - q = - p`
`rarr q - p = 1`