求证不论m为何实属,方程x²+2(m+1)x+2m²+4=0没有实数根
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求证不论m为何实属,方程x²+2(m+1)x+2m²+4=0没有实数根
求证不论m为何实属,方程x²+2(m+1)x+2m²+4=0没有实数根
求证不论m为何实属,方程x²+2(m+1)x+2m²+4=0没有实数根
Δ=4(m+1)²-4(2m²+4)
=4m²+8m+4-8m²-16
=-4m²+8m-12
=-(4m²-8m+4)-8
=-(2m-2)²-8;
∵(2m-2)²≥0恒成立;
所以Δ≤-8<0恒成立;
所以没有实数根
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