#1239 · Algebra · Quadratics

Parameter bounds for real values

Show that the expression $\frac{p x ^{2} + 3 x - 4}{p + 3 x - 4 x ^{2}}$ is capable of all values when $x$ is real, provided that $p$ has any value between $1$ and $7$ .

~15 minProof · checked by AIRange of rational functionsDiscriminant method

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 10

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