由题意知方程x²-(m²+2m-5)x+(m-3)(m²+m-2)=0有两不同实根且x1≤0,x2≥4
令f(x)=x²-(m²+2m-5)x+(m-3)(m²+m-2)
则f(0)≤0,f(4)≤0,
即 (m-3)(m²+m-2)≤0.
16-4(m²+2m-5)+(m-3)(m²+m-2)≤0
一元二次不等式及不等式组当m取任何实数时,不等式x^2-(m^2+2m-5)x+(m-3)(m^2+m-2)
由题意知方程x²-(m²+2m-5)x+(m-3)(m²+m-2)=0有两不同实根且x1≤0,x2≥4
令f(x)=x²-(m²+2m-5)x+(m-3)(m²+m-2)
则f(0)≤0,f(4)≤0,
即 (m-3)(m²+m-2)≤0.
16-4(m²+2m-5)+(m-3)(m²+m-2)≤0