What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

-0.8 and 0.75.

Step-by-step explanation:

20x^4 + x^3 + 8x^2 + x – 12 = 0

by the rational roots theorem:-

The leading coefficient is 20 with factors +/-  1,2,4,5,10,20

and the constant is -12 with factors  +/- 1,2,3,4,6,12

so there are many possible roots like -1, 2, 3/4 3/5 , -4/5 .....

Drawing a graph would be the quickest way to do this,  either manually, using graphical software or a graphical calculator.

I used the latter and got 2 rational roots -0.8 and 0.75.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

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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