Question

If x = p is the H.C.F. of x2 – X – 12 and x2 – 2x – 8,
find value of p.​

Answer 1

Answer:

Answer:

Step-by-step explanation:

let Q(x) = 2 x² - k x - 9 

As (x - k) is a factor of  Q(x),   then Q(k) = 0

Hence,  2 k² - k * k - 9 = k² - 9 = 0    =>   k = +3 or -3

As (x - k) is also factor of P(x) = x² + x - 12,   P(k) = 0.

  P(3) = 3² + 3 - 12 = 0    

  Hence  (x - 3)  is the factor of  P(x) and Q(x).