Please could someone point me in the right direction with this question..
The curve C has equation y = 3x² - 4x + 7. The line L has equation y = 2x + k, where k is a constant.
Given that L and C do not intersect, find the range of possible values of k.
Thanks
The curve C has equation y = 3x² - 4x + 7. The line L has equation y = 2x + k, where k is a constant.
Given that L and C do not intersect, find the range of possible values of k.
Thanks
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Since L and C do not intersect, the equation
3x² - 4x + 7 = 2x + k
has no real solution.
You can rewrite the equation as
3x² - 6x + 7-k = 0
The equation must have no real solution. This means that the discriminant must be negative:
(-6)² - 4*(3)*(7-k) <0
==>36 - 84 +12k < 0
==>12k< 48
==> k< 4
3x² - 4x + 7 = 2x + k
has no real solution.
You can rewrite the equation as
3x² - 6x + 7-k = 0
The equation must have no real solution. This means that the discriminant must be negative:
(-6)² - 4*(3)*(7-k) <0
==>36 - 84 +12k < 0
==>12k< 48
==> k< 4
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3x^2 - 4x + 7 ≠ 2x + k
3x^2 - 6x + 7 ≠ k
As the range of 3x^2 - 6x + 7 is [4,∞), we have k < 4.
3x^2 - 6x + 7 ≠ k
As the range of 3x^2 - 6x + 7 is [4,∞), we have k < 4.