Question

If (x+2a) is a factor of x^5 -4a ^2x^3 +2x + 2a + 3, find a?

Answer 1

Given:

$\sf\ Factor :- x^5 - 4a^2x^3 +2x + 2a + 3$

To Find:

Value of a.

Solution:

$\dashrightarrow\: \sf\ f(x) = x^5 -4a^2x^3 +2x + 2a + 3$

$\dashrightarrow\: \sf\ x+2a = 0$

$\dashrightarrow\: \sf\ x = -2a$

Put this solution in given equation.

$\dashrightarrow\: \sf\ f(-2a)=(-2a)^5 - 4a^2(-2a)^3 +2(-2a) + 2a + 3$

$\dashrightarrow\: \sf\ -32a^5 +32a^5-4a^2a+3$

$\dashrightarrow\: \sf\ -2a+3=0$

$\dashrightarrow\: \sf\ -2a=3$

$\dashrightarrow\: \underline{\boxed{\bf{\orange{a=\frac{3}{2}.}}}}$

$\rule{160}3$

$\large\underline\bold{Additional\: Information}$

• Factor are the numbers you can multiply together to get another number.
• It is very easy to get because we need to find the number by which it is completely divisible.

$\rule{160}3$

Answer 2

Given :

$\sf{ f(x)\: =\: x^5 - 4a^2 x^3 + 2x + 2a + 3}$

⠀

To find :

• Value of a .

⠀

Solution :

➠ $\sf{ f(x)\: =\: x^5 - 4a^2 x^3 + 2x + 2a + 3}$

➠ $\sf{x + 2a = 0}$

➠ $\sf{x = -2a}$

★$\textbf{\small{\green{Putting\: the\: value\: of\: x\: in\: f(x) :}} }$

➠ f(-2a) = (-2a)⁵ - 4a²(-2a)³ + 2(-2a) + 2a + 3

➠ -32a⁵ + 32a⁵ - 4a²a + 3

➠ -2a + 3 = 0

➠ -2a = 3

➠ $\boxed{\underline{\sf{\red{a =\: \frac{3}{2}}}}}$

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