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secondary 3 | A Maths
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Date Posted: 4 years ago
Views: 262
If y does not cut the x-axis (where y = 0), there are no real roots when y is equated to 0
So the discriminant < 0 (b² - 4ac)
(-(6p + 1))² - 4(p - 2)(9p) < 0
(6p + 1)² - (4p - 8)(9p) < 0
36p² + 12p + 1 - 36p² + 72p < 0
84p + 1 < 0
84p < -1
p < -1/84
p - 2 < -2 1/84
This means p - 2 is negative
Since the coefficient of x² = (p - 2) and p - 2 is negative,
Then the coefficient is negative, meaning that y extends downwards (∩ shape)
So it has a maximum point.
So the discriminant < 0 (b² - 4ac)
(-(6p + 1))² - 4(p - 2)(9p) < 0
(6p + 1)² - (4p - 8)(9p) < 0
36p² + 12p + 1 - 36p² + 72p < 0
84p + 1 < 0
84p < -1
p < -1/84
p - 2 < -2 1/84
This means p - 2 is negative
Since the coefficient of x² = (p - 2) and p - 2 is negative,
Then the coefficient is negative, meaning that y extends downwards (∩ shape)
So it has a maximum point.
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Think through what the question is really asking about by visualising the equation given. The boxes are the thought process you should have when seeing these questions.
These questions can only have quadratic equation so always ask yourself the shape of the curve and how the condition given affects the curve in relation to the intersection.
Meaning presence of intersection = presence of roots and no intersection = no roots. Touching one point = 1 repeated root.
What does each mean in terms of b^2-4ac? No roots what’s the condition? Real distinct roots what’s the condition? One repeated root what’s the condition?
These questions can only have quadratic equation so always ask yourself the shape of the curve and how the condition given affects the curve in relation to the intersection.
Meaning presence of intersection = presence of roots and no intersection = no roots. Touching one point = 1 repeated root.
What does each mean in terms of b^2-4ac? No roots what’s the condition? Real distinct roots what’s the condition? One repeated root what’s the condition?
Date Posted:
4 years ago
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