Finding the Minimum Interval of root Equation (Numerical Analysis)

[Ghayyas]

Im New to Numerical Analysis I got a problem, But I don't understand it.
Q: The Minimum interval in which root of the equation x² +3x+1=0 lie is
Options:
1) (0,1)
2) (1,2)
3) (2,4)
4) (0,2)
I think option 1 is correct But I have doubt Please help me to explain this problem.

Please explain Im really confused.

 

[Dr.Peterson]

What method have you been taught to use for this? Technically, the minimum interval containing the roots would be the interval from one root to the other, which is not one of the choices; so you must be referring to the minimum interval obtain by a specific algorithm.

If you can't show any work, can you show an example you were given, or at least name the method?

But there's something wrong with the problem, as neither of the roots lies in any of the given intervals! It's easy to see this, because if x is non-negative, the LHS can never be zero.

 

[HallsofIvy]

By the quadratic formula, \(\displaystyle x= \frac{-3\pm\sqrt{9- 4}}{2}= \frac{-3\pm\sqrt{5}}{2}\). Numerically, those are, to three decimal places, -0.382 and -2.618. As Dr. Peterson said, none of the given intervals includes both roots.

 

[Dr.Peterson]

There are two threads with this same question; in the other, the equation was corrected to [MATH]x^2 - 3x + 1 = 0[/MATH], though that still doesn't make any of the choices valid if the goal is an interval containing both roots.

But I don't think that in either thread Ghayyas has yet clarified the context. Either "minimum interval" is to be taken as "the smallest interval between two integers containing the smaller root" (which would be [0,1], containing 0.382), or as "the smallest interval, obtained by some specific method, containing a root is to be found. Or maybe there's something else.