Question

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

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pls answee fast i have exam tomo​

Answer 1

m = 3, n = 15.

Explanation:

As the factors are z-1 and z+3 then z = 1 and z = -3 are zeroes of the function so substituting for z = 1 and z = -3:

1^3 - 1m - 13(1) + n = 0

n - m = 12...... (a)

(-3)^3 - 9m + 39 + n = 0

n - 9m = -12 ......(b).

Subtract: (a) - (b):

8m = 24

m = 3.

Substituting m = 3 in equation (a):

n - 3 = 12

n = 15.