Question Number 1039 by tera last updated on 22/May/15

jumlah akar−akar persamaan [x]^2 −2[x]−3=0 sama dengan  a.−10          b.−3      e.4  c.−1             d.0

Commented byprakash jain last updated on 22/May/15

[x] =⌊x⌋ =gint(x)?

Commented by123456 last updated on 22/May/15

y=[x]  y^2 −2y−3=0  Δ=(−2)^2 −4(1)(−3)=4+12=16  y=((−(−2)±(√(16)))/(2(1)))=((2±4)/2)=1±2  y_1 =1−2=−1  y_2 =1+2=+3  [x_1 ]=−1⇔−2≤x_1 ≤−1  [x_2 ]=+3⇔3≤x_2 ≤4

Commented byprakash jain last updated on 22/May/15

Please check.  ⌊−2⌋=−2  ⌊−1.5⌋=−2  ⌊x⌋=−1⇒−1≤x<0

Commented by123456 last updated on 23/May/15

what if its is integer part?

Answered by prakash jain last updated on 22/May/15

Taking [x] as floor function  y=⌊x⌋  y^2 −2y−3=0  (y+1)(y−3)=0  y=−1 or y=3  x∈[−1,0)∪[3,4)