Question

Find the monic quadratic with roots a and b, if ab = - 2, a² + b² = 4(a + B)​

Answer 1

Given - a and b are the roots of the equation 2x²+3x+4=0.

So, a+b=(-3/2) and ab=4/2=2

Also, a and b satisfy it. That implies

2a²+3a+4=0 - ( 1 )

And

2b²+3b+4=0 - ( 2 )

Adding equations ( 1 ) and ( 2 ) , we get

2a²+3a+4 + 2b²+3b+4 = 0

2( a² + b² ) + 3( a + b ) + 8 = 0

2( a² + b² ) + 3(-3/2) + 8 = 0

2( a² + b² ) = 9/2 - 8 = - 7/2

( a² + b² ) = -7/4