The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is
A
3
B
2
C
4
D
1
Explanation
$${x^2} - 3\left| x \right| + 2 = 0$$
$$ \Rightarrow {\left| x \right|^2} - 3\left| x \right| + 2 = 0$$
$$\left( {\left| x \right| - 2} \right)\left( {\left| x \right| - 1} \right) = 0$$
$$\left| x \right| = 1,2$$ or $$x = \pm 1, \pm 2$$
$$\therefore$$ No. of solution $$=4$$
4
AIEEE 2003
MCQ (Single Correct Answer)
The value of '$$a$$' for which one root of the quadratic equation
$$$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a - 1} \right)x + 2 = 0$$$
is twice as large as the other is
A
$$ - {1 \over 3}$$
B
$$ {2 \over 3}$$
C
$$ - {2 \over 3}$$
D
$$ {1 \over 3}$$
Explanation
Let the roots of given equation be $$\alpha $$ and $$2$$$$\alpha $$ then