Question

CLASS 9TH MATH
find the value of k if x-3 is a factor of​

Answer 1

Step-by-step explanation:

Given :-

(x-3) is a factor of k²x³-kx²+3kx-k .

To find :-

Fond the value of k ?

Solution :-

Given Cubic polynomial is k²x³-kx²+3kx-k

Let P(x) = k²x³-kx²+3kx-k

Given factor of P(x) = (x-3)

We know that

By Factor Theorem ,

If (x-3) is a factor of P(x) then P(3) = 0

Put x = 3 in the above equation then

=> k²(3)³-k(3)²+3k(3)-k = 0

=> k²(27) - k(9) +9k-k = 0

=> 27k²-9k+9k-k = 0

=> 27k²-10k+9k = 0

=> 27k²-k = 0

=> k(27k-1) = 0

=> k = 0 or 27k-1 = 0

=> k = 0 or 27k = 1

=> k = 0 or k = 1/27

If k = 0 then the given polynomial does not exist .

Therefore, k = 1/27

Answer:-

The value of k for the given problem is 1/27

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.