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+18 votes

The roots of ax2+bx+c=0 are real and positive. a, b and c are real. Then ax2+b|x|+c=0 has 

  1. no roots
  2. 2 real roots
  3. 3 real roots
  4. 4 real roots
asked in Numerical Ability by Boss (17.8k points) | 1.9k views
Answer could be easily obtained via graph.
can u upload sample piece?

4 Answers

+25 votes
Best answer

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.

answered by Veteran (339k points)
selected by
what if n = m ?

ya, that just clicked  ( x - 2 )2 = x2  - 4x + 4  = 0..

In this case Option b could be true.. :)

but here b != 0

Sorry, that was plain wrong. Condition for common root is $b^2 = 4ac$.
@arjun sir

can u explain it more

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

+1 vote
The ans is D  .
answered by Active (1.5k points)
+1 vote
The second equation has both +ve and -ve values of roots of first equation as root.

so it will have 4 roots
answered by Loyal (8k points)
+1 vote

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)

=4 Roots



answered by Active (4.3k points)

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