Question

If x^3-6x^2+11x-6=(x-1)(x-2)(x-a),then a=_____________
please ans fast ​

Answer 1

Answer:

The value of a is 3.

Step-by-step-explanation:

The given equation is x³ - 6x² + 11x - 6 = ( x - 1 ) ( x - 2 ) ( x - a ).

We have to find the value of a.

Now,

x³ - 6x² + 11x - 6 = ( x - 1 ) ( x - 2 ) ( x - a )

LHS = x³ - 6x² + 11x - 6

By factorising the LHS, we get,

x³ - 6x² + 11x - 6

⇒ x³ - ( 5x² + x² ) + ( 6x + 5x ) - 6

⇒ x³ - 5x² - x² + 6x + 5x - 6

⇒ x³ - x² - 5x² + 5x + 6x - 6

⇒ x² ( x - 1 ) - 5x ( x - 1 ) + 6 ( x - 1 )

⇒ ( x - 1 ) ( x² - 5x + 6 )

⇒ ( x - 1 ) ( x² - 3x - 2x + 6 )

⇒ ( x - 1 ) [ x ( x - 3 ) - 2 ( x - 3 ) ]

⇒ ( x - 1 ) ( x - 2 ) ( x - 3 )

RHS = ( x - 1 ) ( x - 2 ) ( x - a )

By equating LHS and RHS, we get,

( x - 1 ) ( x - 2 ) ( x - 3 ) = ( x - 1 ) ( x - 2 ) ( x - a )

⇒ ( x - 3 ) = ( x - a )

⇒ x - 3 = x - a

⇒ - 3 = - a

⇒ a = 3

∴ The value of a is 3.