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JEE Main 202528 JanuaryMorning Shift

Exam: JEE Main
Year: 2025
Date: 28 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Quadratic Equation

JEE Main 2025 · 28 January · Morning Shift · Mathematics · Quadratic Equation

The sum, of the squares of all the roots of the equation x^2+|2...

The sum, of the squares of all the roots of the equation

x^2+|2 x-3|-4=0

, is

Options

A $3(3-\sqrt{2})$
B $6(3-\sqrt{2})$
C $6(2-\sqrt{2})$
D $3(2-\sqrt{2})$

Correct answer

C. $6(2-\sqrt{2})$

Step-by-step solution

\begin{aligned} & \text{ For } x \geq \frac{3}{2} \\ & x^2+2 x-3-4=0 \\ & x^2+2 x-7=0 \\ & x=\frac{-2 \pm \sqrt{4+28}}{2}=-1 \pm 2 \sqrt{2}\end{aligned}

Only

2 \sqrt{2}-1

is acceptable root For

x < \frac{3}{2} x^2-2 x+3-4=0

\begin{aligned} & x^2-2 x-1=0 \\ & x=\frac{2 \pm \sqrt{4+4}}{2}=1 \pm \sqrt{2} \end{aligned}

$

Only

1-\sqrt{2}

is acceptable Sum of the square

=(1-\sqrt{2})^2+(2 \sqrt{2}-1)^2 =6(2-\sqrt{2})$

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