Question

If (x-1) and (x-2) are factors of $x^{3} - 6x^{2} +ax+b$ then the value of a and b

Answer 1

Step-by-step explanation:

Answer

Consider given the expression,

⇒x

3

−ax+b and x−1,x−2 are the factor of this polynomial,

Given that, x−1=0 is the factor of x

3

−ax+b

So, x=1 will be satisfied to x

3

−ax+b

Hence,

1

3

−a.1+b=0

−a+b=−1

a−b=1 ……(1)

Given that, x−2=0 is the factor of x

3

−ax+b

So, x=2 will be satisfied to x

3

−ax+b

2

3

−a.2+b=0

−2a+b=−2

2a−b=2 ……(2)

Subtract equation 1st from equation 2nd,

a=1

put the value of a in equation 1st,

b=0

Hence, this is the answer.

Answer 2

Step-by-step explanation:

Consider given the expression,

⇒x

3

−ax+b and x−1,x−2 are the factor of this polynomial,

Given that, x−1=0 is the factor of x

3

−ax+b

So, x=1 will be satisfied to x

3

−ax+b

Hence,

1

3

−a.1+b=0

−a+b=−1

a−b=1 ……(1)

Given that, x−2=0 is the factor of x

3

−ax+b

So, x=2 will be satisfied to x

3

−ax+b

2

3

−a.2+b=0

−2a+b=−2

2a−b=2 ……(2)

Subtract equation 1st from equation 2nd,

a=1

put the value of a in equation 1st,

b=0

Hence, this is the answer.