f4 maths 緊急!!!

Findth range of values of k when the following statement is true.
a. The graphof y = 2k + 10x - x² doesn't intersect x-axis.
b. Theequation 2x² + 5x - 3k = 0has real roots.

a.
The graph : y = 2k + 10x - x² ...... [1]
x -axis : y = 0 ...... [2]

[1] = [2] :
2k + 10x - x² = 0
x² - 10x - 2k = 0

The graph has two different x-intercepts.
Hence, the discriminant of the above equation Δ > 0
(-10)² - 4(1)(-2k) > 0
100 + 8k > 0
8k > -100
k > -25/2

b.
The equation 2x² + 5x - 3k = 0 has real roots.
Hence, the discriminant of the above equation Δ ≥ 0
(5)² - 4(2)(-3k) ≥ 0
25 + 24k ≥ 0
24k ≥ -25
k ≥ -25/24


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It is given that the graph of y = (k - 1)x² + 3x - 4 has 2 different x-intercepts.
a. can the value of k = 1 ?
b. range of value of k.

a.
When k = 1 :
y = 3x - 4
The graph is a straight line and will have only one x-intercept.

Hence, k is NOT equal to 1.

b.
The graph : y = (k - 1)x² + 3x - 4...... [1]
x-axis : y = 0 ...... [2]

Put [2] into [1] :
(k - 1)x² + 3x - 4 =0

The graph has two different x-intercepts.
Hence, the discriminant of the above equation Δ > 0
(3)² - 4(k - 1)(-4) > 0
9 + 16k - 16 > 0
16k > 7
k > 7/16