Consider the following for the next two (02) items that follow : 

Let Δ(a, b, c, α) = $\left|\begin{array}{ccc} a & b & a \alpha+b \\ b & c & b \alpha+c \\ a \alpha+b & b \alpha+c & 0 \end{array}\right|$

If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ? 

Consider the following for the next two (02) items that follow : 

Let Δ(a, b, c, α) = $\left|\begin{array}{ccc} a & b & a \alpha+b \\ b & c & b \alpha+c \\ a \alpha+b & b \alpha+c & 0 \end{array}\right|$

If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ? 

Consider the following for the next two (02) items that follow :

Given that m(θ) = cot²θ + n²tan²θ + 2n, where n is a fixed positive real number. 

What is the least value of m(θ) ?

Consider the following for the next two (02) items that follow :

Given that m(θ) = cot²θ + n²tan²θ + 2n, where n is a fixed positive real number. 

Under what condition does m attain the least value ?