Question

Q-8 If x+ 2a is a factor of x5 -4a²x³ + 2x+ 2a +3, find the value of a.


(4)

Answer 1

Answer:

Question:If x+2a is a factor of x^5 - 4a^2x^3 + 2x + 2a + 3 find a.To Find:Value of aSolution: x + 2a = 0=> x = - 2aSo we get, ...

Answer 2

Step-by-step explanation:

Given: If x+ 2a is a factor of $x^5 -4a^2x^3 + 2x+ 2a +3$,

To find: Find the value of a.

Solution:

Tip: Apply factor theorem.

Step 1: Put x+2a=0 and find the value of x

$x = - 2a \: ...eq1$

Step 2: Put the value of eq1 in polynomial and find a

${x}^{5} - 4 {a}^{2} {x}^{3} + 2x + 2a + 3 = 0 \\ \\ { (- 2a)}^{5} - 4 {a}^{2} {( - 2a)}^{3} + 2( - 2a)+ 2a + 3 = 0 \\ \\ - 32 {a}^{5} + 32 {a}^{2} {a}^{3} - 4a + 2a + 3 = 0$

because

$\bold{ {x}^{n} . {x}^{m} = {x}^{n + m} }$

Apply the formula

$- 32 {a}^{5} +32 {a}^{5}- 2a + 3 = 0$

Cancel same terms having opposite signs

$\cancel{- 32 {a}^{5}} +\cancel{ 32 {a}^{5}} - 2a + 3 = 0$

$- 2a + 3 = 0 \\ \\ - 2a = - 3 \\ \\ 2a = 3 \\ \\ a = \frac{3}{2}$

Final answer:

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

$\bold{\pink{a = \frac{3}{2} }}$

Hope it helps you.

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