F4 maths y=-2x^2+3x-k-1

(a)

since y = -2x² + 3x - k - 1 cuts the x axis at two points,
the discriminant of -2x² + 3x - k - 1 = 0 is greater than 0
Δ = (3)² - 4(-2)(- k - 1) > 0
9 - 8k - 8 > 0 => 1 > 8k => k < 1/8

(b)

for the largest integral of k in (a), k = 0,
the parabola becomes y = -2x² + 3x - 1.
for x intercepts, y = 0 => -2x² + 3x - 1 = 0
2x² - 3x + 1 = 0 => (2x - 1)(x - 1) = 0 => x = 1/2 or x = 1