An interesting one....

Interesting....and the ans. is B?

pls mention the appraoch too........wud be helpful for others

Here goes...

solutions of the equation 4x^2 + 5x + 1 = 0 are -1/4 and -1

AM = (-1/4+-1)/2 = -5/8
GM = (-1/4*-1)^1/2 = 1/2
HM (in case of two nos.) = 2a*b/(a+b)
HM = (2*-1/4*-1)/(-1/4+-1) = -2/5

arocks...ur method is the conventional one...what if the solutions had surds/complex numbers???

there is a better and an easier way...

yep...i realize this might not be the fastest approach....what do you think is the best/shortest way to crack this? Thanks.

lets c for other responses....other math gurus pls comment...

jangojess wrote:arocks...ur method is the conventional one...what if the solutions had surds/complex numbers???

there is a better and an easier way...

Well to b on the safe side i would go with arocks method .. it doesnt matter if the roots are surds or complex numbers it can still be solved rightly by the "conventional" method .. anyway another method to approach this problem is ..

Divide the given quadratic equation 4x^2 + 5x + 1 = 0. by 4 and we have x^2+5/4*x+1/4 ... Let the roots be m,n

.. Now, for any quadratic equation of the form x^2+a*x+b with the roots m,n , we have a = - (m+n) that is sum of roots and b = m*n that is multiplication of the roots ..

Use this in our quadratic equation and we have m+n = -5/4 and m*n = 1/4 ..

AM = (m+n)/2 = -5/8
GM = root(m*n) = root(1/4) = 1/2
HM = 2mn/(m+n) = (2*1/4)/(-5/4) = -2/5 ..

Well, this method makes it easier in the sense that it saves u the time that u spend calculating the roots of the equation ..

u got it gabriel...this method saves a lot of time and savinng time is really imp coz u never know in which other Qs (a tuf DS/prob/perm...) u wud've to invest time...so try to save time in as much Qs as possible...

gabriel ..i think this method is the safest too coz there is less calc in this method...u can even go wrong in finding the roots thereby getting wrong results...

This was question that i formed in my mind and thot of sharing with u all!!! So no OAs or any source for this Q...Wud really appreciate if everyone can come up with something like this