Question

f(x) = x3 – 2√2x2 – 2x + 6√2
and g(x) = 2x3– 3x2 + 9x – 25
When f(x) is divided by (x +√2), then we get
remainder R1. Also, when g(x) is divided by (2x -5), we get remainder R2. Find the value of (R1 + R2
-R,R2).

Please answer quickly...20 points​

Answer 1

Hello Mate!

Let the remainder be R1 and R2 as given :

R1 = ax^3 + 3x^2 - 3

Now, x - 4 => x = 4

R1 = a(4)^3 + 3(4)^2 - 3

R1 = 64a + 48 - 3

R1 = 64a + 45

R2 = 2x^2 - 5x + a

R2 = 2(4)^2 - 5(4) + a

R2 = 32 - 20 + a

R2 = 12 + a

R1 + R2 = 0

64a + 45 + 12 + a = 0

65a = - 57

a = - 57/65

2R1 - R2 = 0

2( 64a + 45 ) - 12 - a = 0

128a + 90 - 12 - a = 0

127a = - 78

a = - 78/127

But friend, same question I have also done but there is a slight difference in question. In my book there is 2x^3 - 5x + a instead of 2x^2 - 5x + a. So, I am giving pic of that too.

✴ If you had written 2x^2 instead of 2x^3 by mistake then refer to pic.

✴If not, then refer to text I wrote

Hope it helps☺!✌