If the roots of the equation 8x2+6x+a=0  are of the form α and α2, Then the value of a  is

The given equation is 8x2+6x+a=0 The given roots are α and α2 Sum of the roots : α+α2=  34 Product of the roots : α×α2=  a8 α+α2=  34  cubing on both sides, we get  α3+α6+3αα2(α+α2)  =  2764 ⇒    α3  +(α3)2  +3α3(α+α2)=  2764 ⇒    a8  +a264+3a8  (34)=  2764        (∵  α3= a8)                  ⇒    a2+26a−27=0  ⇒a2+27a−a−27=0 ⇒(a−1)(a+27)=0 ∴ a=1,−27