meorifaust
Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A 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 :

xenia168

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
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.