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2022-04-01

For which value of b function

Tristatex9tw

Beginner2022-04-02Added 18 answers

Step 1

We need${a}^{2}-b>0$ , that is ${a}^{2}>b$

$a}^{2}-b\le {m}^{2$

$b\ge {a}^{2}-{m}^{2}$

In summary,

$b\in [{a}^{2}-{m}^{2},{a}^{2})$

We need

In summary,

Jaslyn Allison

Beginner2022-04-03Added 13 answers

Step 1

The discriminant must be positive, i.e.

${a}^{2}-b>0$

The maximum difference of the roots is 2m, and the minimum difference is zero when${a}^{2}-b\to 0$ . So

$0<2\sqrt{{a}^{2}-b}\le 2m$

$0<{a}^{2}-b\le {m}^{2}$

$-{m}^{2}\le b-{a}^{2}<0$

$a}^{2}-{m}^{2}\le b<{a}^{2$

Hence,

$b\in [{a}^{2}-{m}^{2},{a}^{2})$

The discriminant must be positive, i.e.

The maximum difference of the roots is 2m, and the minimum difference is zero when

Hence,

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