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 determinant

Δ = $\left|\begin{array}{lll}\text{a}_{11} & \text{a}_{12} & \text{a}_{13} \\ \text{a}_{21} & \text{a}_{22} & \text{a}_{23} \\ \text{a}_{31} & \text{a}_{32} & \text{a}_{33}\end{array}\right|$

If a13 = yz, a23 = zx, a33 = xy and the minors of a13, a23, a33 are respectively (z − y), (z − x), (y − x) then what is the value of Δ ?

What is the value of a11C11 + a12C12 + a13C13 ?

What is the value of $a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}$?