求證方程2mx平方-3(m+2)x+m+4=0(m為實數)一定有實數根

求證方程2mx平方-3(m+2)x+m+4=0(m為實數)一定有實數根


判別式△=[3(m+2)]²;-4×2m×(m+4)=9m²;+36m+36-8m²;-32m=m²;+4m+36
=(m+2)²;+32
∵無論m取何值,總有△>0
∴方程2mx平方-3(m+2)x+m+4=0(m為實數)一定有實數根



計算:3x^3×(-1/9x^2)


原式
=3×(-1/9)×x^3/x^2
=-1/3*x



分解因式6X^3-9x^2+3x


6X^3-9X^2+3x =6X^3-6X^2-3x^2+3x =6x^2(x-1)-(3x^2-3x)=6x^2(x-1)-3x(x-1)=(6x^2-3x)(x-1)=3x(2x-1)(x-1)