The roots of ax2+bx+c=0 are real and positive. a, b and c are real. Then ax2+b|x|+c=0 has
Let the positive roots be m and n. Now, -m and -n will also satisfy the equation ax2+b|x|+c=0 and hence we have 4 roots.
ya, that just clicked ( x - 2 )2 = x2 - 4x + 4 = 0..
In this case Option b could be true.. :)
but here b != 0
@ Arjun Sir, please comment on this doubt:
A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.
The given equation is quadratic and so depending on discriminant we have
1. b2 −4ac < 0 There are no real roots.
2. b2 −4ac = 0 There is one real root.
3. b2 −4ac > 0 There are two real roots.
you are right...
but this is not simply a quadratic equation.
if we consider it as quadratic equation considering |x| as x, you will get two roots which are real (given in the question )
just because of x^2 and |x|
negative values of above roots(which you have got) also satisfy the above equation
hence total 4 roots
That I understood
ax2+b|x|+c=0 as x<0 => ax2-bx+c=0 ( Two Roots)
x>=0 => ax2+bx+c=0 (Two Roots)