Question

(4) cmr: pt sau luôn có nghiệm ∀m

a) \(x^2+2\left(m-1\right)x-2m-3=0\)

b) \(x^2+\left(2m-1\right)x+2m-2=0\)

c) \(x^2-2\left(m+1\right)+2m-2=0\)

d) \(x^2-2\left(m+1\right)x+2m=0\)

e) \(x^2-2mx+m-7=0\)

f) \(x^2-2\left(m-1\right)x-3-m=0\)

giúp mk vs ạ mk cần gấp

Answer 1

\(a,\Delta=4\left(m-1\right)^2-4\left(-2m-3\right)=4m^2-8m+4+8m+12\\ \Delta=4m^2+16>0\left(đpcm\right)\\ b,\Delta=\left(2m-1\right)^2-4\left(2m-2\right)=4m^2-4m+1-8m+8\\ \Delta=4m^2-12m+9=\left(2m-3\right)^2\ge0\left(đpcm\right)\\ c,Sửa:x^2-2\left(m+1\right)x+2m-2=0\\ \Delta=4\left(m+1\right)^2-4\left(2m-2\right)=4m^2+8m+4-8m+8\\ \Delta=4m^2+12>0\left(đpcm\right)\\ d,\Delta=4\left(m+1\right)^2-4\cdot2m=4m^2+8m+4-8m\\ \Delta=4m^2+4>0\left(đpcm\right)\\ e,\Delta=4m^2-4\left(m+7\right)=4m^2-4m+7=\left(2m-1\right)^2+6>0\left(đpcm\right)\\ f,\Delta=4\left(m-1\right)^2-4\left(-3-m\right)=4m^2-8m+4+12+4m\\ \Delta=4m^2-4m+16=\left(2m-1\right)^2+15>0\left(đpcm\right)\)