Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

It is given a polynomial f(x) = 2x³ + ax² - bx + 12, where a and b are constants. When f(x) is divided by x-2, the remainder is -18. It is known that f(x) is divisible by x + 4. a) Find the values of a and b b) Solve the equation f(x) = 0​

Sagot :

Answer:

Step-by-step 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

View image xenia168
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.