If sin α and cos α are the roots of the equation ax2 +bx+c=0, then

. Since, sin α and cos α are the roots of the equation ax2+ bx+ c=0, then,sin⁡α+cos⁡α=−ba and sin⁡αcos⁡α=caTo eliminate α we have1=sin2⁡α+cos2⁡α⇒     1=(sin⁡α+cos⁡α)2−2sin⁡αcos⁡α⇒    1=b2a2−2ca⇒     a2−b2+2ac=0