if (x-b) is a factor of p(x)=x²+ax-20,then show that b = 20/a+b≠0
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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
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