Let m and n be the numbers of real roots of the quadratic equations x²-12 x+[x]+31=0 and x²-5|x+2|-4=0 respectively, where [x] denotes the greatest integer ≤ x. Then m²+mn+n² is equal to _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q45

JEE Main 20238 Apr, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let m and

\mathrm{n}

be the numbers of real roots of the quadratic equations

x^{2}-12 x+[x]+31=0

and

x^{2}-5|x+2|-4=0

respectively, where

[x]

denotes the greatest integer

\leq x

. Then

\mathrm{m}^{2}+\mathrm{mn}+\mathrm{n}^{2}

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.