Question

Q1. If (x + k) is a factor of 2x2 + 2kx + 5x + 10, ſind k.​

Answer 1

We have to find the value of  k  if  (x + k)  is a factor of  p(x) = 2x² + (2k + 5)x + 10 = 0.

We know that if (x - a) is a factor of a polynomial f(x), then f(a) will be 0.

So, since (x + k) is a factor of p(x), then p(-k) will be 0.  So,

    p(-k) = 0

⇒  2(-k)² + (2k + 5)(-k) + 10 = 0

⇒  2k² - 2k² - 5k + 10 = 0

⇒  10 - 5k = 0

⇒  5k - 10 = 0

⇒  k - 2 = 0

⇒ k = 2

Hence, 2 is the answer.