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Question Number 18432 by Joel577 last updated on 21/Jul/17

Find interval p so (p − 2)x^2 + 2px + p − 1 = 0 have negative roots

Findintervalpso(p−2)x2+2px+p−1=0havenegativeroots

Answered by 433 last updated on 21/Jul/17

Δ≥0 4p^2 −4(p−1)(p−2)≥0 4(p^2 −p^2 +3p−2)≥0 3p−2≥0 ⇒ p≥ (3/2) (1) x_1 x_2 >0 & x_1 +x_2 <0 ((p−1)/(p−2))>0 & −((2p)/(p−2))<0 (p−1)(p−2)>0 & 2p(p−2)>0 p∈(−∞,1)∪(2,+∞) & p∈(−∞,0)∪(2,+∞) (2) (1),(2) p∈(2,+∞)

Δ⩾04p2−4(p−1)(p−2)⩾04(p2−p2+3p−2)⩾03p−2⩾0⇒p⩾32(1)x1x2>0&x1+x2<0p−1p−2>0&−2pp−2<0(p−1)(p−2)>0&2p(p−2)>0p∈(−∞,1)∪(2,+∞)&p∈(−∞,0)∪(2,+∞)(2)(1),(2)p∈(2,+∞)

Commented by Joel577 last updated on 25/Jul/17

thank you very much

thankyouverymuch

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