Question

f x+ 2a is a factor of x5 – 4a2x
3 + 2x + 2a + 3, find a

Answer 1

Step-by-step explanation:

To find :

f (x+ 2a) is a factor of x⁵ – 4a²x³ + 2x + 2a + 3, find a

Solution :

Let g(x) = x⁵ – 4a²x³ + 2x + 2a + 3

f(x) = x + 2a

$⟹ \: \: \: \: \: \: {\bold{\rm{\orange{f(x) \: = \: x \: + \: 2a}}}}$

$⟹ \: \: \: \: \: \: {\bold{\rm{\orange{x \: + \: 2a \: = \: 0}}}}$

$⟹ \: \: \: \: \: \: {\bold{\rm{\orange{x \: = \: -2a}}}}$

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

Thus p(-2a) = 0

${\bold{\rm{⟹ \: \: \: \: \: \: (-2a)⁵ \: - \: 4a² \: (-2a)³ \: + \: 2(-2a) \: + \: 2a \: + \: 3 \: = \: 0}}}$

${\bold{\rm{⟹ \: \: \: \: \: \: -32a⁵ \: + \: 32a⁵ \: - \: 4a \: + \: 2a \: + \: 3 \: = \: 0}}}$

${\bold{\rm{⟹ \: \: \: \: \: \: -2a \: + \: 3 \: = \: 0}}}$

${\bold{\rm{⟹ \: \: \: \: \: \: a \: = \: \frac{3}{2}}}}$

Answer 2

Answer:

given

x + 2a = 0  

=> x = - 2a  

so we get x = -2a  

now set in  

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

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

=> -4a + 2a + 3  

=> - 2a +3  

now  

- 2a + 3 =0  

=> a = -3/-2 = 3/2  

value of a is = 3/2

Step-by-step explanation:

thanks..