If ax2 + 2a2 x + b3 is divisible by (x + a) then …………A) a2 + a

1.	If ax2 + 2a2 x + b3 is divisible by (x + a) then …………A) a2 + ab + b2 = 0 B) a = bC) either a = b or a2 + ab + b2 = 0 D) neither a = b nor a2 + ab + b2 = 0
Answer» Correct option is (C) either a = b or a² + ab + b² = 0 Given that \(ax^2 + 2a^2 x + b^3\) is divisible by (x+a). i.e., x = -a is a zero of \(ax^2 + 2a^2 x + b^3\) \(\therefore\) \(a(-a)^2+2a^2\times-a+b^3=0\) \(\Rightarrow\) \(a^3-2a^3+b^3=0\) \(\Rightarrow\) \(b^3-a^3=0\) \(\Rightarrow\) \((b-a)(b^2+ab+a^2)=0\) \(\Rightarrow\) Either b - a = 0 or \(b^2+ab+a^2=0\) \(\Rightarrow\) Either b = a or \(a^2 + ab + b^2 = 0\) Correct option is C) either a = b or a² + ab + b² = 0

If ax2 + 2a2 x + b3 is divisible by (x + a) then …………A) a2 + ab + b2 = 0 B) a = bC) either a = b or a2 + ab + b2 = 0 D) neither a = b nor a2 + ab + b2 = 0

Answer»

Correct option is (C) either a = b or a² + ab + b² = 0

Given that \(ax^2 + 2a^2 x + b^3\) is divisible by (x+a).

i.e., x = -a is a zero of \(ax^2 + 2a^2 x + b^3\)

\(\therefore\) \(a(-a)^2+2a^2\times-a+b^3=0\)

\(\Rightarrow\) \(a^3-2a^3+b^3=0\)

\(\Rightarrow\) \(b^3-a^3=0\)

\(\Rightarrow\) \((b-a)(b^2+ab+a^2)=0\)

\(\Rightarrow\) Either b - a = 0 or \(b^2+ab+a^2=0\)

\(\Rightarrow\) Either b = a or \(a^2 + ab + b^2 = 0\)

Correct option is C) either a = b or a² + ab + b² = 0