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Mariana [72]
2 years ago
13

Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"​

Mathematics
1 answer:
Sati [7]2 years ago
4 0

Answer:

Let p(x) = x3 + ax2 + bx +6

(x-2) is a factor of the polynomial x3 + ax2 + b x +6

p(2) = 0                                                                                      

p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0

7 +2 a +b = 0

b = - 7 -2a -(i)                                                                              

x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.

p(3) = 3                                                                                      

p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3

11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)                                    

Equating the value of b from (ii) and (i) , we have

(- 7 -2a) = (-10 - 3a)

a = -3                                                                                          

Substituting a = -3 in (i), we get

b = - 7 -2(-3) = -7 + 6 = -1

Thus the values of a and b are -3 and -1 respectively.

Step-by-step explanation:

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Veseljchak [2.6K]

<u>Answer:4.75</u>

<u>Since we don't have a total cost we will write an equation that will allow us to find the cost of x. The equation is 4x= 2x + $3 + $3.75 + $2.75. Now that we have our equation we are going to start by adding 3, 3.75, and 2.75. When added together, they come out with a total of 9.5. Now the equation becomes 4x= 2x + $9.50. Since we have our new equation we are going to subtract 2x from both sides of the equation. We now have the equation 2x= $9.50. Finally, you will divide both sides by 2. This leaves us with the final outcome x= $4.75. This means that one glues stick cost $4.75. Let's check by substituting $4.75 as the value of x in the expressions 4x is Carlo's total and 2x + $3 + $3.75 + $2.75 is Helen's total. First we do 4x, 4 multiplied by 4.75 equals 19, so Carlo spent $19 on art supplies. Now we do 2x + $3 + $3.75 + $2.75, which is 9.5 added to 9.5 and equals 19. So Helen spent $19 on art supplies. This proves that the cost of one glue stick, x, is equal $4.75.</u>

<u></u>

<u></u>

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