According to the rational root theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.

–4, –3, 2, 3, 4
which are actual roots of f(x)?
a) –4 and 3
b) –4, 2, and 3
c) –3 and 4
d) –3, 2, and 4

ANSWER

The actual roots are and .

EXPLANATION

The given function is

According to the rational roots theorem, if is a potential rational root and , then is an actual root.

So we have to plug in all the possible rational roots to see which of them will evaluate to zero.

Evaluating at

Evaluating at

Evaluating at

Evaluating at

Evaluating at

Since and , the actual roots are;

and .

ANSWER

The actual roots are and .

EXPLANATION

The given function is

According to the rational roots theorem, if is a potential rational root and , then is an actual root.

So we have to plug in all the possible rational roots to see which of them will evaluate to zero.

Evaluating at

Evaluating at

Evaluating at

Evaluating at

Evaluating at

Since and , the actual roots are;

and .

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm