Answer:
Let's work out the intercepted points:
-4x + 8 = -3x^2 + 5x + 2
<=>
3x^2 - 9x + 6 = 0
<=>
x^2 - 3x + 2 = 0
<=>
(x - 1)(x - 2) = 0
<=>
x = 1 => y = -4 x 1 + 8 = 4 => A(1, 4)
and
x = 2=> y = -4 x 2 + 8 = 0 =>B(2, 0)
Then, length of chord AB is calculated by:
L = sqrt [(2 - 1)^2 + (0 - 4)^2)] = ~4.123
