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If p and q are the roots of the quadratic equation \(ax^2 + bx + c = 0\), where \(a*b*c ≠ 0\), is the product of p and q greater than 0?
(1) \(|p + q| = |p| + |q|\)
(2) \(ac > 0\)
(1) \(|p + q| = |p| + |q|\)
(2) \(ac > 0\)
28 May 2022, 10:58
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Asked: If p and q are the roots of the quadratic equation \(ax^2 + bx + c = 0\), where \(a*b*c ≠ 0\), is the product of p and q greater than 0?
pq = c/a
p + q = - b/a
(1) \(|p + q| = |p| + |q|\)
p & q have same sign
pq > 0
SUFFICIENT
(2) \(ac > 0\)
Since ac>0, a & c have same sign.
pq = c/a >0
SUFFICIENT
IMO D
pq = c/a
p + q = - b/a
(1) \(|p + q| = |p| + |q|\)
p & q have same sign
pq > 0
SUFFICIENT
(2) \(ac > 0\)
Since ac>0, a & c have same sign.
pq = c/a >0
SUFFICIENT
IMO D
28 May 2022, 11:03
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Since p and q are the roots of quadratic equation given, therefore product of the roots is equal to c/a
PQ=C/A
Option 1 : |P +Q| =|P| + |Q|
This is possible only the numbers are of same sign, either positive or negative.
Therefore if we consider this option only then it is clear that PQ will be positive.
Option 2 : ac>0
This is possible when A & C both are of same sign, either positive or negative.
Therefore if we consider this option only then a/c, which is basically product of the two roots P & Q, will be positive because both A & C are of same sign.
Hence each statement alone is sufficient.
Posted from my mobile device
Since p and q are the roots of quadratic equation given, therefore product of the roots is equal to c/a
PQ=C/A
Option 1 : |P +Q| =|P| + |Q|
This is possible only the numbers are of same sign, either positive or negative.
Therefore if we consider this option only then it is clear that PQ will be positive.
Option 2 : ac>0
This is possible when A & C both are of same sign, either positive or negative.
Therefore if we consider this option only then a/c, which is basically product of the two roots P & Q, will be positive because both A & C are of same sign.
Hence each statement alone is sufficient.
Posted from my mobile device
