Question

if x+2x is a factor of x^5-4a^2x^3+2x+2a+3 find a.

Answer 1

Answer: The value of a is 0.98 and -1.04 .

Step-by-step explanation:

Since we have given that

x+2 is a factor of $x^5-4a^2x^3+2x+2a+3$

So, use $x+2=0\\\\x=-2$

Our equation becomes,

$x^5-4a^2x^3+2x+2a+3=0\\\\(-2)^5-4a^2(-2)^3+2\times -2+2a+3=0\\\\-32+4a^2\times 8-4+2a+3=0\\\\-32+32a^2-4+2a+3=0\\\\32a^2+2a-33=0$

By using quadratic formula, we get,

$a=0.98,a=-1.04$

Hence, the value of a is 0.98 and -1.04 .

Answer 2

"x + 2a = 0

=> x = - 2a

Now keep this value in given expression,

$x^5-4a^2x^3+2x+2a+3$

$= ( -2a )^5 - 4. a^2 .( -2a )^3 + 2 ( -2a ) + 2a + 3$

$= - 32a^5 + 32a^5 - 4a + 2a + 3$

=  -4a + 2a + 3

=  - 2a +3

Then equate this value to 0

- 2a + 3 =0

a = -3/-2 = 3/2

a = 3/2"