Question

The polynomial 2x3+mx2+nx-2 when divided by (2x-3), leaves remainder 7 and has

(x+2) as its factor. Find m and n​

Answer 1

The value of m is "3" and the value of n is "-3".

Explanation:

Let P(x) = 2x3 + mx2 + nx – 2

When P(x) is divided by 2x – 3

P(3/2) = 2(3/2)^3 + a(3/2)^2 + b(3/2) – 2 = 7

= 27/4 + 9/4m + 3/2n – 2 = 7

= 27 + 9m + 6n – 8/4 = 7

= 9m + 6n = 28 + 8 – 27

= 9m + 6n = 9

⇒ 3m + 2n = 3      ….(1)

Similarly now divide the P(x) by (x + 2)

x = - 2

2(- 2)3 + m(- 2)2 + n(- 2) – 2 = 0

-16 + 4m – 2n – 2 = 0

⇒ 4m – 2n = 18     ….(2)

Solving the equations (1) and (2) we get

3m + 2n = 3

4m - 2n = 18

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7m = 21

m = 3

Substitute the value of m in equation 1.

3 x 3 + 2b = 3

2n = 3 – 9

n =  -6/2 = - 3  

n = - 3

m = 3, n = - 3