Question

Qusa
f x-a is a factor of x^3-ax² + 2x +a-1,
find the value of a​

Answer 1

Given:-

• P(x) = x - a
• f(x) = x³ - ax² + 2x + a - 1

To Find:-

• The Value of "a".

Theorem used:-

• Factor theorem.

Now,

→ x - a = 0

→ x = a

Now Putting the value of x in P(x).

→ P(x) = x³ - ax² + 2x + a - 1

→ P(a) = (a)³ - a(a)² + 2(a) + a - 1

→ a³ - a³ + 2a + a - 1

→ 2a + a - 1 = 0

→ 3a - 1 = 0

→ 3a = 1

→ a = 1/3

Hence, The Value of a is 1/3.

Q. ) What is factor theorem ?

→ The factor theorem states that Polynomial has a factor if and only if.

Answer 2

Given:-

• p(x) = x-a

• f(x) = x3-ax2+2x+a -1

To Find :-

• The value of a in the equation

Solution :-

We are given with polynomials and we need to Find the value of a in the equation,

• x-a = 0

• x = a

Substitute the value of x in p( x )

Now,

• p(x) = x3-ax2 + 2x + a-1

• => 2a +a -1 = 0

• 3a - 1 = 0

• 3a = 1

• a = 1/3

So, hence the value of a = 1/3

$\sf{ \bold{ \blue{the \: value \: of \: x = \frac{1}{3} }{} }{} }{}$