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secondary 3 | A Maths
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Date Posted: 3 years ago
Views: 178
equate the two lines then used discriminat> 0 because of the two intersections to find range of k
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Date Posted:
3 years ago
It should be discriminant (b² - 4ac) > 0 for 2 distinct real roots. The = is for real and equal roots only (i.e intersect at 1 common tangent point)
Also what we can realise is that the (k - 3)² can be factored out already without having to expand, and then factorise again.
2x² + (k - 3)x + (k - 3) = 0
Since the line and curve intersect at two distinct points, there are real and distinct roots. discriminant (b² - 4ac) > 0
(k - 3)² - 4(2)(k - 3) > 0
(k - 3)(k - 3 - 8) > 0
(k - 3)(k - 11) > 0
k - 3 < 0 or k - 11 > 0
(Positive coefficient of x² means the parabola opens upwards)
k < 3 or k > 11
2x² + (k - 3)x + (k - 3) = 0
Since the line and curve intersect at two distinct points, there are real and distinct roots. discriminant (b² - 4ac) > 0
(k - 3)² - 4(2)(k - 3) > 0
(k - 3)(k - 3 - 8) > 0
(k - 3)(k - 11) > 0
k - 3 < 0 or k - 11 > 0
(Positive coefficient of x² means the parabola opens upwards)
k < 3 or k > 11
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