Question

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

Answer 1

$\huge \mathfrak{answer : }$

$\sf \large{ \boxed{ \underline{ \underline{ \purple{ \sf{ \: a = 3 \: }}}}}}$

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$\huge \mathfrak \red{Given : }$

• if x² - x - 6 and x² + 3x -18 have a common factor (x - a)

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$\huge \mathfrak \pink{To \: find : }$

• value of a

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$\huge \mathfrak \orange{solution : }$

$\: \: \: \sf \implies{ {x}^{2} - x - 6 = {x}^{2} - 3x + 2x - 6}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = x(x - 3) + 2(x - 3)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = (x + 2)(x - 3) \: ..............(1)}$

$\sf \implies \blue{ {x}^{2} + 3x - 18 = {x}^{2} + 6x - 3x - 18}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \blue{ = x(x + 16) - 3(x + 6)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \blue{ = (x + 6)(x - 3).............(2)}$

• Now we have to compare equation (1) and (2) for the common factor we get,

$\rm{a = 3}$

Answer 2

Answer:

a= -6

Explanation:

x-a becomes

x=a

so now x²-x-6

=a²-a-6

=a²-a=6 1

and x²+3x-18

=a²-3a-18

=a²-3a=18 2

Now from 1 = 2 we get

=18+3a-a=6

=2a=6-18

= a=12/2

= a= -6

Hope it helps you