Question

find the values of m and n so that the polynomial p(x)=z^3-mz^2-13z+n has (z-1) and (z+3) as factors


please answer fast urgent needed please answer fast urgent need please​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• A Cubic Polynomial is given as shown
• $p(x) = {z}^{3} - m {z}^{2} - 13z + n$
• Having Factors ( z-1 ) and ( z + 3 )

To Find:

• The value of m and n in the given cubic Polynomial

Solution:

( z-1 ) and ( z+3 ) are the factors of P(x)

Then z = 1 and z = -3 must be it's zeros

Putting z = 1 in P(x)

$p(x) = {z}^{3} - m {z}^{2} - 13z + n$

$p(1) = {(1)}^{3} - m {(1)}^{2} - 13(1) + n$ -------(1)

$1 - m - 13 + n = 0$

$n - m = 12$ ---------(3)

Similarly putting z = ( -3 ) in p(x)

$p( - 3) = {( - 3)}^{3} - m {( - 3)}^{2} - 13( - 3) + n$

$( - 27) - m(9) - 13( - 3) + n = 0$

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

$9m - n = 12$ ---------(4)

____________________________

Solving equation (3) and (4)

Multiplying by 9 in equation (3) and adding with equation (4)

$(9n - 9m) + (9m - n) = 108 + 12$

$8n = 120$

$n = 15$

Putting n= 15 in equation (3) we get

$n - m = 12$

$15 - m = 12$

$m = 3$

Hence value of m and n are 3 and 15 respectively

Answer 2

Step-by-step explanation:

hope it helps you

m=3

n=15