Question

if ax²+2a²x+b³ is divisible by x+a then​

Answer 1

Answer:

Step-by-step explanation:

If ax² + 2a²x + b³ is divisible by x + a, then x + a is a factor of ax² + 2a²x + b³. Also the value of polynomial will be zero when x = -a.

=> a(-a)² + 2a²(-a) + b³ = 0

=> a³ - 2a³ + b³ = 0

=> b³ - a³ = 0

=> a³ - b³ = 0

We know that a³ - b³ = (a - b)(a²+ab + b²)

=>  (a - b)(a²+ab + b²) = 0

=> a - b = 0 or a² + ab + b² = 0

=> a = b or a² + ab + b² = 0

Thus it mean a= b or a² + ab + b² = 0, when ax²+2a²x + b³ is divisible by x + a.