If (x+l) ( x+m) = x^2 + 4x + 2 find the value of (l -m)^2 ?
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Expanding the Polynomial
x² + lx + mx +lm =x² +4x +2
lx + mx + lm=4x+2
x(l+m) + lm = 4x + 2
By comparing the coef. of x and constant term
l+m=4 and lm=2
(l+m)²=4² ⇒l² + m² +2lm = 16
l² + m² =16 - 2lm=16 - 4 = 12
We know l² + m² -2lm=(l-m)²
so 12 - 4=(l-m)²
Hence (l-m)²=8
x² + lx + mx +lm =x² +4x +2
lx + mx + lm=4x+2
x(l+m) + lm = 4x + 2
By comparing the coef. of x and constant term
l+m=4 and lm=2
(l+m)²=4² ⇒l² + m² +2lm = 16
l² + m² =16 - 2lm=16 - 4 = 12
We know l² + m² -2lm=(l-m)²
so 12 - 4=(l-m)²
Hence (l-m)²=8
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