Question

. If (x-1) and (x-2) are factors of the polynomial (x-1)(x²-kx+2),then the value of k is​

Answer 1

Given:

p(x)=(x-1)(x^2-kx+2)

• Factors of p(x) are (x-1) and (x-2)

⇒ (x=1) or (x=2)

• Substitute ‘x=2’ value in p(x)

⇒ p(2)=(2-1)(2^2-k(2)+2)=0

⇒ 1(4-2k+2)=0

⇒ 6-2k=0

⇒ -2k=-6

⇒ 2k=6

⇒ k=6/2

⇒ =

• Proof that my answer is correct:

• Put ‘k’ value in p(x) and substitute x=2

⇒ p(x)=(x-1)(x^2-3x+2)

⇒ p(2)=(2-1)(2^2-3(2)+2)

⇒ p(2)=1(4-6+2)

⇒ p(2)=6-6

⇒ p(2)=0

Hope it helped....