Question
Question: Two real numbers a and b are such that a + b = 3 & \|a – b\| = 4, then a&b are the roots of the quad...
Two real numbers a and b are such that a + b = 3 & |a – b| = 4, then a&b are the roots of the quadratic equation -
A
4x2 –12x – 7 = 0
B
4x2 – 12x + 7 = 0
C
4x2 –12x + 25 = 0
D
None of these
Answer
4x2 –12x – 7 = 0
Explanation
Solution
a + b = 3 |a – b| = 4
a2 + b2 + 2ab = 9 …(i)
a2 +b2 –2ab=16 ..(ii)
4 ab = – 7 Ž ab = –7/4
x2 – (a + b) + ab = 0 Ž x2 –3x – 7/4 = 0
4x2 –12x – 7 = 0