設(shè)方程x²+xcosθ+sinθ=0與x²+xsinθ+cosθ=0相同的實(shí)根為a
故：a²+acosθ+sinθ=0,a²+asinθ+cosθ=0
兩式相減：a(cosθ-sinθ)+( sinθ- cosθ)=0
故：(a-1)(cosθ-sinθ)=0
故：a-1=0或cosθ-sinθ＝0
（1）當(dāng)cosθ-sinθ＝0時(shí),即：tanθ=1,因?yàn)棣取蔥0.2π],故：θ＝π/4或5π/4,此時(shí)x²+xcosθ+sinθ=0與x²+xsinθ+cosθ=0完全一樣,有無數(shù)個(gè)相同的實(shí)根,符合
（2）當(dāng)a-1=0時(shí),即a=1時(shí),則1²+cosθ+sinθ=0,故：cosθ+sinθ=-1
故：sin(θ+π/4)=-√2/2
因?yàn)棣取蔥0.2π],故：θ+π/4=5π/4,或θ+π/4=7π/4
故：θ=π/2或θ=3π/2
故：θ＝π/4或θ＝5π/4或θ=π/2或θ=3π/2