Question

IF X CUBE +ax square - bx+ 10 divided by x square -3x +2 find a and b

Answer 1

Question :-

If x^3 + ax^2 - bx + 10 is divided by x^2 - 3x + 2 . find a and b.

Solution :-

Since,

x^3 + ax^2 -bx + 10 is divided by x^2 -3x + 2

therefore,

the remainder on dividing will be zero.

Dividing

x^3 + ax^2 - bx + 10 by x^2 - 3x + 2

__________________

x^2-3x+2 ) x^3 + ax^2 - bx + 10 ( x+(a+3)

x^3 - 3x^2 + 2x

- + -

______________________

x^2(a+3) -x(b+2) +10

x^2(a+3) -3x(a+3) + (2a+6)

- + -

_____________________

x(-b-2+3a+9) + ( -2a+4)

we have the remainder

x(3a-b+7) + ( -2a+4)

equating it with zero

x (3a-b+7) + (-2a+4) = 0

x(3a-b+7) + ( -2a + 4) = 0.x + 0

comparing LHS and RHS

-2a + 4 = 0

-2a = - 4

a = 2

Also

3a - b + 7 = 0

3 ( 2) - b + 7 = 0

- b = - 13

b = 13 .

therefore,

the value of a is 2

and

b is 13 .