Expert Answer to "If x-2 is a factor of x2-bx+b where..."

ge2szesup2

Answered question

2023-02-03

x - 2

is a factor of

x^{2} - b x + b

where

b

is constant, what is the value of

b

acropole191

Beginner2023-02-04Added 4 answers

Calculating c's value:
Using the factor theorem: If

P (x)

is polynomial of degree

n \geq 1

and

a \in R

, then

(x - a)

is a factor of

P (x)

, if

P (a) = 0

∴

(x - 2)

is a factor of

P (x) =

x^{2} - b x + b

, if

P (2) = 0

\Rightarrow P (2) = 0

\Rightarrow x^{2} - b x + b = 0

For

x = 2

\Rightarrow 2^{2} - b \times 2 + 2 = 0

\Rightarrow 2^{2} - b \times 2 + b = 0 \Rightarrow 4 - 2 b + b = 0 \Rightarrow 4 - b = 0 \Rightarrow b = 4

Therefore, the value of

b

4

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?