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1. (4 points) Given that 1 + 2i is a root of the polynomial P (x) = 4x4 −

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Batory AA HL Short Test 3 April 3, 2020

Name:

1. (4 points) Given that 1 + 2i is a root of the polynomial P (x) = 4x4 − 24x3 + 69x2 − 114x + 85 find the other roots.

(2)

Batory AA HL Short Test 3, page 2 of 4 April 3, 2020

2. (6 points) (a) Show that:

cos

arcsin x + arcsin

x 2

=

√1 − x2

4 − x2 − x2 2

(b) Hence find the value of cos

arcsin

3 21

+ arcsin

3 2

21

(c) Hence write down the value of arcsin

3 21

+ arcsin

3 2

21

(3)

Batory AA HL Short Test 3, page 3 of 4 April 3, 2020

3. (4 points) Solve:

3 + 3 cos x = 2 sin2x for 0 ¬ x ¬ 4π.

(4)

Batory AA HL Short Test 3, page 4 of 4 April 3, 2020

4. (6 points)

(a) Show that 1

sin2x + 1

cos2x = 4 sin22x.

(b) Hence find the exact solutions to the equation 1

sin2x + 1

cos2x = 16 3 for −π < x < π.

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