Question

if x+1 is a factor of P(x) = 3x² - kx, then find the value of k​

Answer 1

Step-by-step explanation:

Given :-

x+1 is a factor of P(x) = 3x² - kx

To find :-

Find the value of k ?

Solution :-

Given Quadratic Polynomial P(x) = 3x²-kx

Given factor of P(x) = x+1

We know that

Factor Theorem :-

Let P(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.

Given that

(x+1) is a factor of P(x)

=> P(-1) = 0

(Since x+1 = 0 => x = -1)

=> P(-1) = 3(-1)²-k(-1) = 0

=> 3(1)-(-k) = 0

=> 3-(-k) = 0

=> 3+k = 0

=> k = 0-3

=> k = -3

Therefore, k = -3

Answer:-

The value of k for the given problem is -3

Check:-

If k = -3 then

P(x) = 3x²-(-3)x

=> P(x) = 3x²+3x

=> P(x) = 3x(x+1)

=>(x+1) is one of the factors of P(x).

Verified the given relation. in the given problem

Used formulae:-

Factor Theorem :-

• Let P(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.