Question

if x-3 is a factor of x ^2 + kx +9 , then find the value of k​

Answer 1

x=3 then put the values of x in the equation and equal to 0

3^2+3k+9=0

3k=-18

k= -6

whenever you find these type of questions , just put the value of x in the equation and you will find your answer immediately

Answer 2

Given :

(x-3) is a factor of x² + Kx +9

To Find :

The value of K

Theory :

The factor theorem states that if f(x) is a polynomial of degree n ≥1 and 'a' is any real number, then (x-a) is a factor of f(x) if f(a)=0.

Solution :

Let F(x)= x²+Kx+9

It is given that (x-3) is a factor of F(x)

Thus , by factor theorem ;

F(3)= 0

(3)²+K(3)+9= 0

9+3k+9=0

18=-3K

K= -6

Hence , the value of K is -6