Question

The polynomials p(x)=4x^2-px+5 and g(x)=x^3+6x^2+p leave the remainders a and b respectively by (x+2). FInd the value of p if a+b=0
Please give the answer fast...Very Urgent...Please and Thank You

Answer 1

Step-by-step explanation:

Remainder theorem:

When we divide f(x) by (x−c) , the remainder is equal to f(c)

When p(x)=4x

3

−2x

2

+px+5 is divided by (x+2), the remainder is

p(−2)=4(−2)

3

−2(−2)

2

+p(−2)+5

=−2p−35

So,

a=−2p−35

When q(x)=x

3

+6x

2

+p is divided by (x+2), the remainder is

q(−2)=(−2)

3

+6(−2)

2

+p

=p+16

So,

b=p+16

Now,

a+b=0

−2p−35+p+16=0

−p−19=0

p=−19

Answer 2

Answer:

Step-by-step explanation:

Given that,

Let p ( x ) = 4x² - px + 5 = a

If ( x +2 ) is a factor of p ( x ) , then

x + 2 = 0 ⇒ x = - 2 .

On substituting " x = - 2 " in p (x ) ,we get

p (- 2 ) = 4 ( - 2 )² - p ( - 2 ) + 5 = a

⇒ 4 ( 4 ) + 2p + 5 = a ( ∵ - × - = + )

⇒ 16 + 2p + 5 = a

⇒ 2p + 21 = a

Let g ( x ) = x³ + 6x² + p = b

∴ g ( - 2 ) = ( - 2 )³ + 6 ( - 2 )² + p = b ( ∵ x + 2 = 0 ⇒ x = - 2 )

⇒ - 8 + 6 ( 4 ) + p = b

⇒ - 8 + 24 + p = b

⇒ 16 + p = b

∴ a + b = 0

⇒ 2p + 21 + p+ 16 = 0

⇒ 3p + 37 = 0

⇒ 3p = - 37

⇒ p = - 37 / 3 is the answer.