Question

if x^2-x-6 and x^2+3a-18 have a common factor (x-a) then find the value of a​

Answer 1

Answer:

3

Step-by-step explanation:

(x - a) is factor of both x^2 - x - 6 and x^2 + 3x - 18, means when x = a, value of these polynomials is 0.

So, for x = a,

a^2 - a - 6 = 0 & a^2 + 3a - 18 = 0

Subtract one from another:

=> (a^2 - a - 6) - (a^2 + 3a - 18) = 0

=> - 4a + 12 = 0

=> a = 3

Answer 2

Answer:

$\huge \fbox {3}$

$\small \blue {(x - a) \: is \: a \: factor \: of \: both \: x^2-x-6 \: and \: x^2+3a - 18 \: which \: means \: x = \: a}$

$\small \red {Thus \: the \: value \: of \: polynomial \: is \: 0}$

$\longrightarrow subtraction$

➡️ $( a^2 - a - 6) - (a^2 + 3a - 18)$

➡️ $-4a \: + 12 \: = \: 0$

➡️$a \: = \frac{12}{4}$

➡️$a \: = 3$