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Trigonometric Functions and Equations question

2024 · 4 Apr · Shift 2 · Q51

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JEE Main
Mathematics
Trigonometric Functions and Equations
2024 · 4 Apr · Shift 2 · Q51

Trigonometric Functions and Equations question

2024 · 4 Apr · Shift 2 · Q51

JEE MainMathematicsTrigonometric Functions and EquationsNumerical+4 / −1

Let

S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\left(\sin ^6 \theta+\cos ^6 \theta\right)=0\right.

has real roots

\}

. If

\alpha

and

\beta

be the smallest and largest elements of the set

S

, respectively, then

3\left((\alpha-2)^2+(\beta-1)^2\right)

equals

\underline{\hspace{2cm}}

.

Numerical answer

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