If ax^2+2a^2x+b^3 is exactly divisible by x+a,then prove that a=b or a^2+ab+b+ab+b^2=0
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Step-by-step explanation:
Since ax
2
+2a
2
x+b
3
is divisible by x+a, f(−a)=0.
∴ a(−a)
2
+2a
2
×−a+b
3
=0.
∴ −a
3
+b
3
=0.
∴ (b−a)(b
2
+ab+a
2
)=0.
∴b=a or b
2
+ab+a
2
=0.
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