Which is larger, the sum of the roots of equation A or the

Question

A: x^2 + 6x - 40 = 0
B: x^2 + kx + j = 0

Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?

(1) j = k

(2) k is negative

fluke · Answer

Sum of roots of an equation:
 ax^2+bx+c=0 
Is
 \frac{-b}{a}

So,

A.  x^2 + 6x - 40 = 0 
Sum of roots =\frac{-6}{1}=-6

B.  x^2 + kx + j = 0 
Sum of roots =\frac{-k}{1}=-k

We need to find 
Larger of (-6, -k)

1.  j=k 
k can be 100 or -100.
Not Sufficient.

2. k<0
Thus, -k>0
Any positive number will always be greater than -6.
Thus, -k > -6
OR
Sum of roots of B > Sum of roots of A
Sufficient.

Ans: "B"

yogesh1984 · Answer

Funnily enough I could not move on this till clock ticked one minutes then I moved to shortcuts (lazy me

) and picked B (obviously I was not sure though!) but when I saw only this part- sum of root = -b/a (Fluke's explanation) I was like ok I have done it right :lol:

Spidy001 · Answer

Sum of roots = -b/a

A Sum of roots = -6
B sum of roots = -k

so the comparison is between -6 and -k , to see which one is greater

1. Not sufficient
j=k

k=2 => -k>-6 = > B>A
k=8 => -k<-6 =>B<A

2. Sufficient

As k is negative -k is always going to be positive
=> -k is always greater than -6
=> sum of roots of B is always greater than sum of roots of A.

Answer is B.

petrifiedbutstanding · Answer

Fluke,

Can you please explain the part show in the question better? I didn't understand how you obtained a positive number

dimri10 · Answer

to petrifiedbutstanding i'll try: 
if k is negative
thenthe equation looks like: X^2 -kx + j = 0

so the sum of roots is: (minus)- (b)/(a) or in our case -(minus) (-k)/1
which makes it: --(minus minus) k/1 or +k which is a positve number.

if k is a positive number it will allways be bigeer than -6

williambrubaker · Answer

I don't understand how j and k could be anything other than 4. Can anybody give me roots of this equation other than 2 that both add to and multiply to the same number?

Bunuel · Answer

Why should the roots the roots add to and multiply to the same number?

Also, note that we are not told that j and k are integers...

Which is larger, the sum of the roots of equation A or the

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