If the roots of the equation x^2-px+q differ by unity then
(a)p^2=4q
(b)p^2=4q+1
(c)p^2=4q-1
(d)p=q
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Answer:Let the roots be a and b
a - b = 1. as given roots differ by unity
a + b = p
ab = q
a - b = √ {( a+b)² - 4ab}
1 = √{ ( -p)² - 4( q ) }
Squaring both sides
p² = 1+4q. hence, proved
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