Question

If x-1is the root polynomial of p(x)=8x cube-ax square-x+2

Answer 1

Hey friend, Harish here.

Here is your answer.

Given that :

x - 1 is the root of the polynomial p(x) = 8x³ - ax² - x + 2

To Find :

The value of a.

Solution :

As (x - 1) is a root of p(x). Then it must divide p(x) perfectly leaving no remainder.

Now according to remainder theorem

Dividend = Divisor . Quotient + remainder.

Here, Dividend = p(x) , Divisor = (x - 1) , quotient  - not known , remainder = 0.

Therefore ,

Dividend = Divisor . Quotient

Let us assume Divisor = 0. Then dividend is also zero.

Which means:   (x - 1) = 0 , and x = 1

Then , p(1) = 0 = 8(1)³ - a(1)² - (1) + 2

⇒ 8 - a + 1 = 0

⇒ a = 9 .

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Hope my answer is helpful to you.