Page 213 - aljaber

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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