If-f-x-ax-2-bx-c-g-x-ax-2-bx-c-where-ac-0-then-f-x-g-x-0-has-

Tinku Tara June 14, 2023 None 0 Comments

Question Number 109485 by ZiYangLee last updated on 24/Aug/20

If f(x)=ax^2 +bx+c, g(x)= −ax^2 +bx+c where ac ≠ 0, then f(x)g(x)=0 has

$$\mathrm{If}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c},\:{g}\left({x}\right)=\:−{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{where}\:{ac}\:\neq\:\mathrm{0},\:\mathrm{then}\:{f}\left({x}\right){g}\left({x}\right)=\mathrm{0}\:\mathrm{has} \\ $$

Answered by ajfour last updated on 24/Aug/20

f(x)g(x)=h(x)=(bx+c)^2 −a^2 x^4 has no real roots, one real root or two real roots, not more.

$${f}\left({x}\right){g}\left({x}\right)={h}\left({x}\right)=\left({bx}+{c}\right)^{\mathrm{2}} −{a}^{\mathrm{2}} {x}^{\mathrm{4}} \\ $$$${has}\:{no}\:{real}\:{roots},\:{one}\:{real}\:{root}\:{or} \\ $$$${two}\:{real}\:{roots},\:{not}\:{more}. \\ $$

Commented by ZiYangLee last updated on 24/Aug/20

$$\mathrm{thanks} \\ $$

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