Question

If x 2 -3x+2 is a factor of polynomial x 4 -ax 3 +b, then find the value of a and b

Answer 1

x²-3x + 2
= x²- 2x -1x + 2
= x(x-2) -1 (x-2)
= (x-1).(x-2)

x-2 = 0 (remainder theorem)
x=2

x⁴-ax³+ b =0
2⁴-2³a + b =0
16-8a + b =0
8a-b = 16.............. eq. I

x-1 =0 (remainder theorem)
x=1

x⁴-ax³+b =0
1⁴ - 1³a + b =0
1 - a + b = 0
a-b = 1................eq. II

8a-b = 16
- a-b = 1
- + -
___________
7a = 15

a= 15 ÷ 7
a = 2.14285714
a = 2.14

a-b =1
a-1 =b
b = 2.14-1
b =1.14

8a-b =16
8(2.14) -16 =b
b = 8[ (2.14)-2 ]
b = 8 (0.14)
b = 1.12

Answer 2

If x 2 -3x+2 is a factor of polynomial x 4 -ax 3 +b, then find the value of a and b

1

SEE

x²-3x + 2

= x²- 2x -1x + 2

= x(x-2) -1 (x-2)

= (x-1).(x-2)

x-2 = 0 (remainder theorem)

x=2

x⁴-ax³+ b =0

2⁴-2³a + b =0

16-8a + b =0

8a-b = 16.............. eq. I

x-1 =0 (remainder theorem)

x=1

x⁴-ax³+b =0

1⁴ - 1³a + b =0

1 - a + b = 0

a-b = 1................eq. II

8a-b = 16

- a-b = 1

- + -

___________

7a = 15

a= 15 ÷ 7

a = 2.14285714

a = 2.14

a-b =1

a-1 =b

b = 2.14-1

b =1.14

8a-b =16

8(2.14) -16 =b

b = 8[ (2.14)-2 ]

b = 8 (0.14)

b = 1.12