To ensure that rs <0, the r and s must be of opposite sign. Which means b^2 - 4c > b^2 [ as per Quadratic equation solution]
Which means c < 0. Hece statement 2 is alone sufficient.
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Root
Source: Beat The GMAT — Data Sufficiency |
Solution of x^2+bX+c=0 will be
(-b+(b^2-4c)^1/2)/2 = r
(-b-(b^2-4c)^1/2)/2 = s
so r*s = b^2-(b^2-4c)/4
=> rs = 4c/4 = c
means rs is equal to C.
1) value of b will not affect value of rs - NOT SUff
2) value of C will direclt effect rs - Answer
Answerd : B.
(-b+(b^2-4c)^1/2)/2 = r
(-b-(b^2-4c)^1/2)/2 = s
so r*s = b^2-(b^2-4c)/4
=> rs = 4c/4 = c
means rs is equal to C.
1) value of b will not affect value of rs - NOT SUff
2) value of C will direclt effect rs - Answer
Answerd : B.
Shubham.
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To ensure that rs <0, the r and s must be of opposite sign. Which means b^2 - 4c > b^2 [ as per Quadratic equation solution]
Which means c < 0. Hece statement 2 is alone sufficient.
Which means c < 0. Hece statement 2 is alone sufficient.
If r and S are the roots of the quadratic equation x^2+bX+C = 0 ...(1)
then (X-r)(X-s)=0
Upon simplification
X^2 -(r+s)x+rs = 0 ....(2)
Comparing (2) with (1)
b= -r-s
c=rs
Case 1
b<0 => -r-s<0 => Implies nothing ...insuff
Case 2
c<0 => rs< 0 => suff
Hence B
then (X-r)(X-s)=0
Upon simplification
X^2 -(r+s)x+rs = 0 ....(2)
Comparing (2) with (1)
b= -r-s
c=rs
Case 1
b<0 => -r-s<0 => Implies nothing ...insuff
Case 2
c<0 => rs< 0 => suff
Hence B
