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Answer:
Given : line y=mx+4 intersects the curve y=3x2 −4x+7at two distinct points.
To find : set of values of m
Step-by-step explanation:
y = mx + 4
y = 3x² − 4x + 7
Substitute y = mx + 4 to find intersection point
mx + 4 = 3x² − 4x + 7
=> 3x² - x(m + 4) + 3 = 0
(m + 4)² > 4(3)(3)
=> m² + 8m + 16 > 36
=> m² + 8m - 20 > 0
=> (m + 10)(m - 2) > 0
m < - 10 & m > 2
m = (-∞ , - 10) ∪ ( 2 , ∞ )