# Number of values of the parameter #alpha in [0, 2pi]# for which the quadratic function, # (sin alpha) x^2 + 2 cos alpha x + 1/2 (cos alpha +sin alpha)# is the square of a linear function is? (A) 2 (B) 3 (C) 4 (D) 1

##### 1 Answer

Mar 5, 2017

See below.

#### Explanation:

If we know that the expression must be the square of a linear form then

then grouping coefficients we have

so the condition is

This can be solved obtaining first the values for

We know that