Question

find the value of k if x-3is a factor of k^2x^3-x^2+3x-1​

Answer 1

Answer:

Let p(x) = k2x2−kx−2.

According to factor tbeorm, x=(−3) as (x-3) is a factor of p(x).

According to remainder theorm,p(-3)=0.

So,

p(-3) = 0 = k2x2−kx−2

⟹k2x2−kx−2=0

⟹k2x2−kx=2

⟹k2(−3)2−k(−3)=2

⟹k29+3k−2=0

⟹9k2+3k−2=0

⟹9k2+6k−3k−2=0

⟹3k(3k+2)−1(3k+2)=0

⟹(3k+2)(3k−1)=0

⟹k=−2/3or1/3.

Answer 2

Answer:

(x-3) is a factor of f(x)=k^2.x^2-k.x-2 , thus , f(3)= 0

f(3)=k^2.(3^2)-k.3–2=0

or. 9k^2–3k-2=0

or. 9k^2–6k+3k -2=0

or. 3k(3k-2)+1(3k-2)=0

or. (3k-2).(3k+1)=0

k = 2/3. , -1/3. Answer.