Question

find the value of a and b so that the polynomial x³+10x²+ax+b is exactly divisible by x-1 as well as x-2​

Answer 1

Step-by-step explanation:

x³ + 10x² + ax + b exactly divisible by x - 1

x - 1 = 0

x = 1

1³ + 10(1)² + a(1) + b = 0

1 + 10 + a + b = 0

11 + a + b = 0

a + b = -11 equ (1)

x³ + 10x² + ax + b = 0 exactly divisible by x-2

x - 2 = 0

x = 2

2³ + 10(2)² + a(2) + b = 0

8 + 40 + 2a + b = 0

48 + 2a + b = 0

2a + b = - 48 equ (2)

subtract (1) from (2)

2a + b = - 48

-(a + b = - 11)

a = - 37

substitute a = -37 in equ (1)

a + b = - 11

-37 + b = - 11

b = - 11 + 37

b = 26

therefore a = - 37 and b = 26

Hope you get your answer