Trigonometric Functions · Question 26

If [-2 , 2 ], then the number of solutions of 2 2 2 + (2 - 6) - 3 = 0, is equal to:

1. 8
2. 6
3. 10
4. 12

Answer

(1) 8

Solution

Let c = : 2 2c2 + (2 - 6)c - 3 = 0

Discriminant D = (2 - 6)2 + 4(2 2)( 3) = 10 - 4 6 + 8 6 = 10 + 4 6 = (2 + 6)2

c = -(2 - 6) (2 + 6)4 2

c = 2 64 2 = 32 or c = -44 2 = - 1 2

In [-2 , 2 ] (two full periods of ), each value in (-1, 1) is taken 4 times:

= 32: = 6, 11 6 (4 solutions)

= - 1 2: = 3 4, 5 4 (4 solutions)

Total number of solutions = 8

Answer: (1)