F.4 Maths

2a+3 ad 2b+3 are the roots of x^2 + 2x - 7 = 0
Therefore,
Sum of roots = -b/a = -2
2a+3 + 2b+3 = -2
2a + 2b + 6 = -2
2a + 2b = -8
a + b = -4
Product of roots = c/a = -7
(2a+3)(2b+3) = -7
4ab + 6b + 6a + 9 = -7
4ab + 6(a+b) = -16
4ab + 6(-4) = -16
4ab - 24 = -16
4ab = 8
ab = 2

If a^2 and b^2 are the roots of an equation, to find this...
Sum of roots = a^2 + b^2
= a^2 + 2ab + b^2 - 2ab
= (a+b)^2 - 2ab
= (-4)^2 - 2(2)
= 16 - 4
= 12
Product of roots = a^2 b^2
= (ab)^2
= 4

Thus, the equation must be x^2 - 12x + 4 = 0