Write a polynomial in factored form with least possible degree having zeros at 5, -2 multiplicity 3, -3 multiplicity 2, 3i multiplicity 2, and f(-1)=-800.

Polynomial:

Step-by-step explanation:

Zeros are at 5, (-2 * 3 = -6), (-3 * 2 = -6), (3i * 2 = 6i)

= 5, -6, -6, and 6i

The factors are (x-5), (x-(-6)), (x-(-6)), (x-6i)

= (x-5), (x+6), (x+6), (x-6i)

For f(-1) = -800, x = -1 which gives a factor of (x - (-1)) = x + 1. The remainder is -800

The polynomial is thus:

f(x) = (x+1)(x-5)(x+6)(x+6)(x-6i) - 800

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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