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

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

= - 4 ( given: f(x) is divisible by x + 4 )

= 0.5

= 3

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

false

step-by-step explanation:

rulers and compasses arent required in order to bisect an angle because when bisecting angles, you're making a "half circle" and considering in order to bisect an angle it wouldn't be straight, you wouldn't need either of the two