Question

if alpha and beta are the roots of x2+7x +3=0 then (alpha -1)2 +(beta -1)2=

Answer 1

alpha and beta are the roots of
x² + 7x + 3 = 0

alpha + beta= -7
alpha.beta = 3

now,
( alpha -1 )² + ( beta - 1)²
=alpha² -2alpha.1 +1 + beta² -2.beta .1 + 1
={ alpha² + beta² } -2( alpha + beta) +2
={ (alpha +beta)²-2alpha.beta } -2( alpha + beta ) +2
={ (-7)² -2(3)} -2(-7) +2
={ 49 -6} +14 +2
=43 +16
=59

Answer 2

Hola amigo ,

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x²+7x+3=0
ATQ α+β=$\frac{-b}{a}$=-7
and   αβ=$\frac{c}{a}$=3
Now,
=(α-1)(β-1)2
=(αβ-α-β+1)2
=[αβ-(α+β)+1]2
=[3-(-7)+1]2
=11x2
=22
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