Question

find the value of a if (x+2a) is the factor of x^4-2ax^3+2x+2a+3

Answer 1

Answer:

Let p(x)=x

5

−4a

2

x

3

+2x+2a+3 and g(x)=x+2a

Now. g(x)=x+2a

x+2a=0

x=−2a

Now, if g(x) is a factor of p(x), then p(−2a) must be 0

Thus, p(−2a)=0

=>(−2a)

5

−4a

2

(−2a)

3

+2(−2a)+2a+3=0

=>−32a

5

+32a

5

−4a+2a+3=0

=>−2a+3=0

=>a=

2

3

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