Question

Can any one explain it step by step? Plz do answer it.​

Answer 1

ANSWER:-

Given:

If the polynomial (az)³ +(4z)² +3z -4 & z³-4z =0 leave the same remainder when divided by z-3.

To find:

Find the value of a.

Solution:

⚫Let p1(z)= az³ +4z² +3z -4

⚫Let p2(z)= z³ -4z =0

When we divide p1(z) by z-3,

So, remainder is p1(3).

Now,

p1(3) = a(3)³ +4(3)² + 3(3) -4

p1(3) = 27a + 36 +9 -4

p1(3) = 27a +36 + 5

p1(3) = 27a + 41.

&

Similarly, remainder p2(3)

Now,

p2(3) = (3)³ - 4(3) +a

p2(3) = 27 - 12 +a

p2(3) = 15 + a

According to the question:

both the remainder are same,

p1(3) = p2(3)

=) 27a +41 = 15 + a

=) 27a -a = 15 -41

=) 26a = -26

=) a= -26/26

=) a= -1

Hence,

The value of a is -1.

Hope it helps ☺️