Verified answer

Answer:

a = -17 and b = 12

Step-by-step explanation:

3x³+2x²+ax+b = 0

Substitute the values of x-1 = 0 or x = 1 and x+3=0 or x = -3

For x=1

• 3x³+2x²+ax+b = 0
• 3(1)³+2(1)²+a(1) +b = 0
• 3(1)+2(1)+a+b=0
• 3+2+a+b = 0
• 5+a+b = 0
• a+b = -5

For x=-3

• 3x³+2x²+ax+b=0
• 3(-3)³+2(-3)²+a(-3)+b=0
• 3(-27)+2(9)-3a+b=0
• -81+18-3a+b=0
• -63-3a+b=0
• -3a+b = 63

We solve the system of linear equations:

• a+b = -5 and -3a+b = 63

a+b = -5

a = -b-5

let's substitute it to the other equation

• -3a+b = 63
• -3(-b-5) + b = 63
• 3b+15+b = 63
• 4b+15 = 63
• 4b = 63-15
• 4b = 48
• b = 48/4
• b = 12

Then solve for a

• a = -b-5
• a = -(12)-5
• a = -12-5
• a = -17

Checking:

• 3x³+2x²-17x+12 = 0

for x = 1

• 3(1)³+2(1)²-17(1)+12=0
• 3+2-17+12=0
• -17+17=0
• 0 = 0

for x = -3

• 3(-3)³+2(-3)²-17(-3)+12=0
• 3(-27)+2(9)+51+12=0
• -81+18+51+12=0
• -81+81=0
• 0=0

Answer:

2ax^{3}+3x^{3}+b

Step-by-step explanation:

sana makatulong pa beainliest pls