Sign of P(Δ) with ²P(x)=ax²+bx+c and Δ=b2−4ac

meteraiqn

meteraiqn

Answered

2022-02-01

Sign of P(Δ) with P(x)=ax²+bx+c and Δ=b24ac

Answer & Explanation

Natalia Thomas

Natalia Thomas

Expert

2022-02-02Added 7 answers

Completing the square differently, this is non-negative when a>0,,Δ0,2b14a0:
1aP(Δ)=Δ2+baΔ2baΔ+b24a2+2baΔb24a2+ca=Δ22b2aΔ+b24a2+2baΔb24ac4a2=(Δb2a)2+(2b14a)Δa1aP(Δ)=Δ2+baΔ2baΔ+b24a2+2baΔb24a2+ca=Δ22b2aΔ+b24a2+2baΔb24ac4a2=(Δb2a)2+(2b14a)Δa

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