Let S= sin ² 2 θ:(sin ⁴ θ+ cos ⁴ θ) x²+(sin 2 θ) x+(sin ⁶ θ+ cos ⁶ θ)=0. has real roots. If α and β be the smallest and largest elements of the set S, respectively, then 3((α-2)²+(β-1)²) equals _ _ _ _ _.

Trigonometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 4 Apr, Evening shift · Q52

JEE Main 20244 Apr, Evening shiftMathematicsMediumTrigonometry118× since 2002

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 __________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2024 Trigonometry Question with Answer (4 Apr Evening shift, Q52) | JEE Arc