f.4,,amathz,,

sum of roots = a + b = -b / a = -(-2) / 1 = 2

product of roots = ab = c / a = -6 / 1 = -6

Sum of roots of the required equation

= (a﹣2b) + (b﹣2a)

= -a﹣b

= -(a + b)

= -2

product of roots of the required equation

= (a﹣2b)(b﹣2a)

= ab﹣2a2﹣2b2 + 4ab

= 5ab﹣2(a2 + b2)

= 5ab﹣2(a2 + b2 + 2ab﹣2ab)
= 5ab﹣2[(a + b)2﹣2ab]
= 5ab﹣2(a + b)2 + 4ab
= 9ab﹣2(a + b)2
= 9(-6)﹣2(2)2
= -62

The required quadratic equation is
x2﹣(Sum of roots)x + product of roots = 0
x2 + 2x﹣62 = 0