Question

if x squar -x-6 and x square -3x-18 have a common factor (x-a) then find the value of a.​

Answer 1

Answer: (-6)

Step-by-step explanation:

Let f(x) = x - a

⇒ 0 = x - a

⇒ x = a

Let p(x) = x² - x - 6

By substituting f(x) in p(x),

⇒ a² - a - 6

Let q(x) = x² - 3x - 18

By substituting f(x) in q(x),

⇒ a² - 3a - 18

According to the question,

$a^{2} -a-6=a^{2} -3a-18\\=>-a-6=-3a-18\\=>18-6=a-3a\\=>12=-2a\\=>a=\frac{12}{-2} =(-6)$

Thanks!!