Question

Previous year IIT jee Question
Chapter :- complex number and quadratic equation​

Answer 1

EXPLANATION.

Number of real solution of the equations.

⇒ x² - 3|x| + 2 = 0.

As we know that,

We can write equation as,

⇒ |x|² - 3|x| + 2 = 0.

Factorizes the equation into middle term splits, we get.

⇒ |x|² - 2|x| - |x| + 2 = 0.

⇒ |x|(|x| - 2) - 1(|x| - 2) = 0.

⇒ (|x| - 1)(|x| - 2) = 0.

⇒ |x| = 1  and  |x| = 2.

⇒ x = ± 1  and x = ± 2.

Hence 4 real solutions exists.

Option [B] is correct answer.

Answer 2

$EXPLANATION.</p><p>Number of real solution of the equations.</p><p>⇒ x² - 3|x| + 2 = 0.</p><p>As we know that,</p><p></p><p>We can write equation as,</p><p>⇒ |x|² - 3|x| + 2 = 0.</p><p></p><p>Factorizes the equation into middle term splits, we get.</p><p>⇒ |x|² - 2|x| - |x| + 2 = 0.</p><p>⇒ |x|(|x| - 2) - 1(|x| - 2) = 0.</p><p>⇒ (|x| - 1)(|x| - 2) = 0.</p><p>⇒ |x| = 1  and  |x| = 2.</p><p>⇒ x = ± 1  and x = ± 2.</p><p></p><p>Hence 4 real solutions exists.</p><p>Option [B] is correct answer.$