Question

If x + 2a is a factor of x⁵ – 4a²x³ + 2x + 2a + 3, find a.

Answer 1

According to the question,

Let p(x) = x⁵ – 4a²x³ + 2x + 2a + 3 and g(x) = x + 2a

g(x) = 0

⇒ x + 2a = 0

⇒ x = –2a

Therefore, zero of g(x) = –2a

We know that,

According to the factor theorem,

If g(x) is a factor of p(x), then p(–2a) = 0

So, substituting the value of x in p(x), we get,

p(–2a) = (–2a)⁵ – 4a²(–2a)³ + 2(–2a) + 2a + 3 = 0

⇒ –32a⁵ + 32a⁵ – 2a + 3 = 0

⇒ –2a = –3

⇒ a = `3/2`