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Functions question

2022 · 28 Jul · Shift 1 · Q43

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JEE Main
Mathematics
Functions
2022 · 28 Jul · Shift 1 · Q43

Functions question

2022 · 28 Jul · Shift 1 · Q43

JEE MainMathematicsFunctionsNumerical+4 / −1

For

\mathrm{p}, \mathrm{q} \in \mathbf{R}

, consider the real valued function

f(x)=(x-\mathrm{p})^{2}-\mathrm{q}, x \in \mathbf{R}

and

\mathrm{q}\gt 0

. Let

\mathrm{a}_{1}

,

\mathrm{a}_{2^{\prime}}\mathrm{a}_{3}

and

\mathrm{a}_{4}

be in an arithmetic progression with mean

\mathrm{p}

and positive common difference. If

\left|f\left(\mathrm{a}_{i}\right)\right|=500

for all

i=1,2,3,4

, then the absolute difference between the roots of

f(x)=0

is

\underline{\hspace{2cm}}

.

Numerical answer

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