Question

Find the set of values of m for which the line with equation y = mx + 1 and the curve with equation y = 3x^2+ 2x + 4 intersect at two distinct points.

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Answer 1

Given : line y=mx+4 intersects the curve y=3x2 −4x+7at two distinct points.

To find : set of values of m

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 , ∞ )