It is given a polynomial f(x) = 2x³ + ax²  bx + 12, where a and b are constants. When f(x) is divided by x2, the remainder is 18. It is known that f(x) is di
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1. User Answers xenia168
Answer:
Stepbystep explanation:
(a). 2( 2 )³ + a ( 2 )²  b ( 2 ) + 12 + ( 18 ) = 0
16 + 4a  2b + 30 = 0
4a  2b =  46
2a  b =  23 ....... ( 1 )
2 (  4 )³ + a (  4 )²  b (  4 ) + 12 = 0
 128 + 16a + 4b + 12 = 0
16a + 4b = 116
4a + b = 29 ........ ( 2 )
( 1 ) + ( 2 )
6a = 6 , a = 1
4(1) + b = 29 , b = 25
(b). 2x³ + x² + 25x + 12 = 0
[tex]x_{1}[/tex] =  4 ( given: f(x) is divisible by x + 4 )
[tex]x_{2}[/tex] = 0.5
[tex]x_{3}[/tex] = 3