determine the value of m and n for mx^3 +20x^2+ nx-36 when divided by (x+1) gives remainder 0 and when divided by (x-2) gives remainder of 45.​

Given:

The given polynomial is

When it divided by (x+1) gives remainder 0 and when divided by (x-2) gives remainder of 45.

To find:

The values of m and n.

Solution:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).

Let the given polynomial be P(x).

When it divided by (x+1) gives remainder 0. So, P(-1)=0.

                  ...(i)

When P(x) is divided by (x-2) gives remainder of 45. So, P(2)=0

                 ...(ii)

Multiply 2 on both sides of (i).

                  ...(iii)

Subtract (iii) from (ii).

Putting m=5.5 in (i), we get

Therefore, the values of m and n are 5.5 and -21.5 respectively.

1/800 is the right answer

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct