Question

If (x-3) is a factor of x -kx -2 then the value of k is

Answer 1

★ Given :

x - 3 is a factor of x² - Kx -2

★ To find :

The value of k

"★ Solution"

If x - 3 is factor of f(x) , then f(3) should be equal to 0 by factor theorem..

f(x) = x² - Kx - 2

f(3) = 3² - k(3) - 2

= 9 - 3k - 2

= 7 - 3k

7 - 3k = 0

7 = 3k

$\purple{\leadsto k = \dfrac{7}{3}}$

★ Additional Information :

Factor theorem : x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number.

Remainder theorem : Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

Answer 2

★Answer:

g(x)=x-3

p(x)=x²-kx-2

g(x)=0

now,

x-3=0

x=3

therefore,

x=3

substitute in p(x)

p(x)=x²-kx-2

p(3)=3²-3k-2

9-3k-2=0

7-3k=0

7=3k

k=7/3