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Quadratic Equation and Inequalities question

2024 · 31 Jan · Shift 2 · Q55

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JEE Main
Mathematics
Quadratic Equation and Inequalities
2024 · 31 Jan · Shift 2 · Q55

Quadratic Equation and Inequalities question

2024 · 31 Jan · Shift 2 · Q55

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1

Let

a, b, c

be the lengths of three sides of a triangle satistying the condition

\left(a^2+b^2\right) x^2-2 b(a+c) x+\left(b^2+c^2\right)=0

. If the set of all possible values of

x

is the interval

(\alpha, \beta)

, then

12\left(\alpha^2+\beta^2\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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