If the roots of ax^2- 4x + b = 0 are 1/2 and 8, what is the value of (a + b)^2?

Let’s start with the given
equation:

ax^2 - 4x + b =0

we
write it as

=> x^2 - (4/a)x + (b/a)
=0

now as -1/2 and -8 are the roots of the equation we
have:

=> (x-1/2)(x-8) = x^2 - (4/a)x +
(b/a)

=> x^2 –(1/2 + 8)x + 4 = x^2 - (4/a)x +
(b/a)

So we have  8+ 1/2 = 4/a and 4 =
b/a

8+ 1/2 = 4/a

=> a =
8/17

b = 4a = 32/17

Therefore
(a + b)^2 = (8/17 + 32/17)^2 = (40/17)^2 = 1600/
289

The value of  (a+b)^2 = 1600/
289