Question

If
$a {x}^{2} + 2 {a}^{2} x + {b}^{3}$
is divisible by x+a then which condition must be true,[a, b>0]
(A)
$a + b = 0$

(B)
${a}^{2} + 2ab + {b}^{2} = 0$
(C)
${a}^{2} - ab + {b}^{2} = 0$
(D)
$a = b$

Answer 1

Answer:

Option (A)

a=-b

According to question both a and b is greater than 0

(A) ××××××××

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(B) a^2 +2ab+b^2=0

(a+b)^2 =0

a+b= 0option A and option B are same

(B)×××××××××××××

__________________________

Option (C)

a^2-ab+b^2=0

(a+b)^2 -3ab=0

(a+b)=√(3ab)

(C)××××××××××

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Option (D)

a=b

ax^2 + 2a^2x +b^3

ax^2 +2a^2x +a^3

a( x^2 +2ax+a^2)

a×(x+a)^2

Option D satisfied the equation

So

Answer is option (D)