Question

if x-3 and x+3 are factors of polynomial x cube-mx square-13x+n find value m n?

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Given :

(x³ - mx² - 13x + n)

Since (x - 3) and (x + 3) are factors of (x³ - mx² - 13x + n), 3 and -3 will satisfy the equation :

x³ - mx² - 13x + n = 0.

When, x = 3, we get :

3³ - m×3² - 13×3 + n = 0

=> 27 - 8m - 39 + n = 0

=>》8m - n = - 12 .....(i)

and

(-3)³ - m×(-3)² - 13×(-3) + n = 0

=> - 27 - 9m + 39 + n = 0

=> - 9m + n = - 12 .....(ii)

Now, adding (i) and (ii), we get :

- m = - 24

=> m = 24

From (i), we get :

8×24 - n = - 12

=> 192 - n = - 12

=> n = 204

Therefore, the values of m and n are 24 and 204 respectively.

♧♧HOPE THIS HELPS YOU♧♧