Question

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Answer 1

Answer:

Option c 1 is the answer

Step-by-step explanation:

First, we have x+2

So,we know p(x) = 0

So,x+2 = 0

Therefore x = - 2

Now, p(x) = x^3-2ax^2+16

p(-2) = (-2)^3-2a(-2)^2+16

(-8)-2a(4)+16 = 0 {as p(x) = 0}

-8 -8a = - 16

-8a = - 16+8

-8a = - 8

a = - 8/-8

Therefore, a= 1

HOPE IT HELPS YOU

THANK YOU............

Answer 2

Given:

• There is a polynomial x³-2ax²+16.
• x+2 is a factor of x³-2ax²+16.

To Find:

• The value of a .

Concept Used:

• We will use 'Factor Theorem ' to find out the value of a .

Answer:

We have been given a polynomial which is x³-2ax²+16. [say p(x)].

Let

• p(x)=x³-2ax²+16.
• g(x)=x-2.

Now ,

(x+2) is a factor of p(x).

So on equating f(x) with 0 ,

$\sf{\implies f(x)=0}$

$\sf{\implies x+2=0}$

${\underline{\red{\sf{\leadsto x =(-2)}}}}$

So, on putting (-2) in x p(x) will be 0.

$\sf{\implies (-2)^{3}-2a\times (-2)^{2}+16=0}$

$\sf{\implies -8-2a\times 4=-16}$

$\sf{\implies -8-8a=-16}$

$\sf{\implies -8a=-16+8}$

$\sf{\implies -8a=-8}$

$\sf{\implies a=\dfrac{-8}{-8}}$

${\underline{\boxed{\red{\sf{\leadsto a=1}}}}}$

Therefore the value of a is 1.