Question

Find the value of a and b if (x-1) and (x-2) are the factors of x³-ax+b

Answer 1

Answer:

Step-by-step explanation:

f(x)=x³-ax+b

g(x)=(x-1)

f(1)=(1)³-a*1+b

   =1-a+b=0

   =b=a-1                                          (  --i  )

g(x)=(x-2)

f(2)=(2)³-a*2+b

    =8-2a+b

from (i)

8-2a+b=0

8-2a+(a-1)=0

8-2a+a-1=0

7-a=0

-a=-7

a=7

b=a-1

 =7-1

 =6

so, a=7 and b=6

Answer 2

Given that

x³ - ax + b is a polynomial

and

(x-1) and (x-2) is the factor

or when we replace x = 1 and x = 2 in above's equation we will get zero

Then by putting x = 1

=> 1³ - a(1) + b = 0

=> 1 - a + b = 0 ....................(i)

Now by putting x = 2

=> 2³ - a(2) + b = 0

=> 8 - 2a + b = 0 ............(ii)

Now by equating (i) and (ii)

=> 1 - a + b = 8 - 2a + b

=> 8 - 1 -2a + a + b - b = 0

=> 7 - a = 0

=> a = 7

then by putting value of a in equation (i)

1 - a + b = 0

=> 1 - 7 + b = 0

=> -6 + b = 0

=> b = 6

Hope it helps