Question

If (x + 1) and (x – 2) are factors of x3 + ax2 – bx – 6, then find the values of a and b respectively.
ANS IS:-
a=2,b=5

Answer 1

Step-by-step explanation:

x=-1

so putting value of x in the equation,

(-1)3+a(-1)2-b×-1-6=0(since it is a factor)

-1+a+b-6=0

a+b=7.....(i)

x=2

putting value again,

(2)3+a(2)2-b×2-6=0

8+4a-2b-6=0

or, 4a-2b+2=0

or,2(2a-b+1)=0

or,2a-b= -1......(ii)

Adding (i) and (ii) we get,

3a=6. | 2+b=7

or,a=2 | b=5 ( answers matched....)

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Answer 2

Step-by-step explanation:

i. x= 1=0

x=-1

(-1)³+a(-1)²-b(-1)-6

-1+a+b-6=0

a+b=7

ii. x-2=0

x=2

(2)³+4a-2b-6=0

4a-2b+2=0

2(2a-b+1)=0

2a-b= -1

Adding (i) and (ii)

3a=6 , 2+b=7

or

a=2 , b=5