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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