If v is chosen at random from {- 3, 0, 1, 10} and w is

Question

If v is chosen at random from {- 3, 0, 1, 10} and w is chosen at random from { - 4 , 3, 7} what is the probability that x^2 + vx + w > 0 for all real numbers x ?

(A) 1/4 (B) 1/3 (C) 5/12 (D) 1/2 (E) 2/3

LM · Answer

Is their a subscript of 2 with the first X ? Please clarify that or is it X*2?

vshaunak@gmail.com · Answer

It should be 1/2.

Total cases = 4*3 = 12

We have to find the values of v and w, for which the equation x^2+vx+w have real roots. It means (v^2 - 4w) should be greater than ZERO.

These value are
V=-3 W =-4
V=0 W =-4
V=1 W =-4
V=10 W =-4
V=10 W =3
V=10 W =7

Hence prob = 6/12 =  1/2

kevincan · Answer

Why would you want the equation to have real roots? I assume you are referring to x^2 + vx + w = 0

PPGJ · Answer

Here is my take :horror

Given that f(x) = x^2 + vx +w = = (x+ v/2)^2 + (w-v^2 /4) Now we know that 1st term = non-negative 2nd term must be +ve too to have f(x) +ve Therefore w - v^2 / 4 > 0 which is equivalent to saying that v^2 < 4w Thus taking v from {- 3, 0, 1, 10} and +ve values for w from {- 4,3,7} When w=3, v^2 < 12 , hence values of v satisfying this ( -3,0,1 ) When w=7, v^2 < 28, hence again 3 values will satisfy this (w will not be equal to -4 because v^2 cannot be < -ve number The total # of cases = 4*3 = 12 Thus Probability = 6/12 = 1/2 Hence (D) Hope got it right :?:

kevincan · Answer

Correct, though it is a bit easier to think in terms of the quadratic formula as vshaunak did. Excellent work

GMATBLACKBELT · Answer

How do you get (v^2-4w) must be greater than 0 from x^2+xv+w????


Can you please elaborate on how you got this. 

Thanks

If v is chosen at random from {- 3, 0, 1, 10} and w is

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