Question

If x+2a is a factor of a^5-4a^2x^3+2x+2a+3, then find the value of a.

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Answer 1

CORRECT QUESTIONS:-

If x+2a is a factor of a⁵-4a^2x³+2x+2a+3, then find the value of a.

EXPLANATION:-

Let:-

p(x)=a⁵-4a^2x³+2x+2a+3 ang g(x)=x+2a

Now let's use remainder theorem:-

x+2a=0

x=-2a

So remainder=p(-2a)=0 (since x+2a is a factor)

Let's find it's value:-

→p(-2a)=(-2a)⁵-4a²(-2a)³+2(-2a)+2a+3

→p(-2a)=-32a⁵+32a⁵-4a+2a+3

→p(-2a)=-2a+3

Since p(-2a)=0 we can write:-

o=-2a+3

2a=3

a=3/2

So value of a is 3/2

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