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. q1(x ) = x − 1 x 2 + 1 x 4 + 1 ()
2 4 16
. r2 = q1 − 1 = (−1) 1 1 = −1
2 2 8 16
:( )
(x2 + 5x + 4 )(x 2 + 5x + 6) + 1 = 0
y = x 2 + 5x
(y + 4)(y + 6) + 1 = 0
y2 + 10y + 25 = 0
(y + 5)2 = 0
y = x 2 + 5x .y1 = y2 = −5
x 2 + 5x + 5 = 0
x = −5 ± 25 − 20 = −5 ± 5
22
x3 = x4 = −5 − 5 x1 = x2 = −5 + 5
2 2
. x1 + x2 + x3 + x4 = −5 + 5 − 5 − 5 = −10
:( ) ( )
( ).r(x) = ax + b f (x) = x 2 − 1 q(x) + r(x)
f (1) = r(1) = a + b
f (−1) = r(−1) = −a + b
. f (−1) = (−1)51 − 1 = −2 f (1) = 151 − 1 = 0
a +b = 0
−a + b = −2