Which of the following equation has maximum number of real roots?

x^{2} - | x | - 2 = 0

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x^{2} - 2 | x | + 3 = 0

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x^{2} - 3 | x | + 2 = 0

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x^{2} + 3 | x | + 2 = 0

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Solution

The correct option is D $x^{2} - 3 | x | + 2 = 0$
$x^{2} - 3 | x | + 2 = 0$

$| x |^{2} - 2 | x | - | x | + 2 = 0$

$| x | (| x | - 2) - 1 (| x | - 2) = 0$

$(| x | - 2) (| x | - 1) = 0$

$| x | = 1, 2$

$x = \pm 1, \pm 2$

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Similar questions

Q. Write the number of real roots of the equation x² + 3 |x| + 2 = 0.

Question 10
Which of the following equations has no real roots?
(A) $x^{2} - 4 x + 3 \sqrt{2} = 0$
(B) $x^{2} + 4 x - 3 \sqrt{2} = 0$
(C) $x^{2} - 4 x - 3 \sqrt{2} = 0$
(D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Q. The equation

x^{2} - 3 | x | + 2 = 0

has

Q. Show that the equation

x^{2} - x + 2 = 0

has no real roots.

Q. The number of real solution of the equation

| x^{2} | - 3 | x | + 2 = 0

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Which of the following equation has maximum number of real roots?

The correct option is D x2−3|x|+2=0x2−3|x|+2=0|x|2−2|x|−|x|+2=0|x|(|x|−2)−1(|x|−2)=0(|x|−2)(|x|−1)=0|x|=1,2x=±1,±2

The correct option is D $x^{2} - 3 | x | + 2 = 0$
$x^{2} - 3 | x | + 2 = 0$

$| x |^{2} - 2 | x | - | x | + 2 = 0$

$| x | (| x | - 2) - 1 (| x | - 2) = 0$

$(| x | - 2) (| x | - 1) = 0$

$| x | = 1, 2$

$x = \pm 1, \pm 2$