Let a, b, c be three non-zero real numbers such that the equation 3acosx+2bsinx=c,x∈-π2,π2 has two distinct real roots α and β with α+β=π3 . Then,  the value of ba is ……

3cosx+2basinx=casince α,β are roots of the above equation ,⇒     3cosα+2basinα=ca →1 and 3cosβ+2basinβ=ca →2now 1-2⇒3[cosα-cosβ]+2ba(sinα-sinβ)=0⇒3-2sinα+β2sinα-β2+2ba2cosα+β2sinα-β2=0⇒-3+23·ba=0⇒ ba=12=0.5       since α+β=π3