Question

if
x^2-x-6 and x² +3x -18 have common
factor (x-a)
then find the value of a
​

Answer 1

Answer:

x(x-3)+2(x-3) =(x-3)(x+2).and x(x+6)-3(x+6)=(x-3)(x+6) so the common factor is (x-3)

Answer 2

$\huge{\underline{\bigstar{\sf{solution!!}}}}$

$let p (x) = {x}^{2} - x - 6 and q (x) = {x}^{2} + 3x - 18$

$if ( x -a) is a factor of p(x), then p(a) = 0$

$({a})^{2} - (a) - 6 = 0$

${a}^{2} - a - 6 = 0$

${a}^{2} - a = 6 (1)$

$if (x-a) is a factor of a (x),then q(a) = 0$

$({a})^{2}+ 3 (a) - 18 = 0$

${a}^{2}+ 3 (a) - 18 = 0$

${a}^{2} + 3a - 18 = 0$

${a}^{2} + 3a = 18 (2)$

$solving \: equations \: we \:get, [tex]</p><p>[tex] {a}^{2} - a = 6$

$- {a}^{2} + 3a= 18$

$(-) (-) (-)$

____________________

$- 4a = -12$

$Therefore a = 3$