Question

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

Answer 1

Answer:

If a,x

2

+b,x+c

1

=0

and a

2

x

2

+b

2

x+c

2

=0

have a common root, then conditions for common root is

∣

∣

∣

∣

∣

∣

1

1

a

2

c

1

c

2

∣

∣

∣

∣

∣

∣

2

=

∣

∣

∣

∣

∣

∣

a

1

a

2

b

1

b

2

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

b

1

b

2

c

1

c

2

∣

∣

∣

∣

∣

∣

In case ,equation are

x

2

+ax+b=0

and x

2

+bx+a=0

∴ for common root

∣

∣

∣

∣

∣

∣

1

1

b

a

∣

∣

∣

∣

∣

∣

2

=

∣

∣

∣

∣

∣

∣

1

1

a

b

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

a

b

b

a

∣

∣

∣

∣

∣

∣

(a−b)

2

=(b−a)(a

2

−b

2

)

(a−b)

2

=−(a−b)(a−b)(a+b)

(a−b)

2

=−(a−b)

2

(a+b)

or (a−b)

2

+(a−b)

2

(a+b)=0

or (a−b)

2

[1+a+3]=0

(a−b)

2

=0

a=b

but ∴a



=b as equation become same

1+a+b+=0

or

a+b=−1