Question

17. Find the values of 'a' and 'b' so that the polynomial (x - 10x +ax+b) is exactly divisible
by (x - 2) as well as (x - 1).​

Answer 1

Answer:

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Step-by-step explanation:

Putting x=2

2+10×2+a×2+b

12+2a+b=0

2a+b=-12

a+b=-12/6

a+b=-2

a=-2-b.......i

putting value in eq.

12+2(-2-b)+b

12-4-2b+b

8-b=0

8=b

b=8

putting this in eq.1

a=-2-8

a=-10

Thereforea=-10 and b= 8

Answer 2

Answer:

a = 9, b = 0

Step-by-step explanation:

though it appears something is missing in the given polynomials, I proceed with what is given.

here f(x) = x - 10x + ax + b

this function will be divisible by x - 2 if f(2) = 0

putting x = 2 in the function we get

2 - 20 + 2a + b = 0

this gives

2a + b = 18...........eqn 1

again the function will be divisible by x - 1 if f(1) = 0

1 - 10 + a + b = 0

this gives

a + b = 9........eqn 2

subtracting eqn 2 from eqn 1, we have

a = 9

which gives b= 0