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secondary 4 | A Maths
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Date Posted: 4 years ago
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Date Posted:
4 years ago
let y = -x² + ax - 6
dy/dx = -2x + a
For y = x - 2, dy/dx = 1
When line is a tangent to the curve, the gradient is the same for both at that point.
So -2x + a = 1
2x = a - 1
x = (a - 1)/2
Since the line is a tangent to the curve, they meet at one point.
So when -x² + ax - 6 = x - 2, there one real and repeated root .
x² + x - ax + 6 - 2 = 0
x² + (1 - a)x + 4 = 0
For one real and repeated root, discriminant = 0
(b² - 4ac = 0)
(1 - a)² - 4(1)(4) = 0
(1 - a)² - 16 = 0
(1 - a)² = 16
1 - a = ±√16 = ±4
a = 1 ± 4
a = -3 or a = 5
dy/dx = -2x + a
For y = x - 2, dy/dx = 1
When line is a tangent to the curve, the gradient is the same for both at that point.
So -2x + a = 1
2x = a - 1
x = (a - 1)/2
Since the line is a tangent to the curve, they meet at one point.
So when -x² + ax - 6 = x - 2, there one real and repeated root .
x² + x - ax + 6 - 2 = 0
x² + (1 - a)x + 4 = 0
For one real and repeated root, discriminant = 0
(b² - 4ac = 0)
(1 - a)² - 4(1)(4) = 0
(1 - a)² - 16 = 0
(1 - a)² = 16
1 - a = ±√16 = ±4
a = 1 ± 4
a = -3 or a = 5
when a = -3,
x = (-3 - 1)/2 = -2
y = -2 - 2 = -4
Coordinates of P are (-2,-4)
x = (-3 - 1)/2 = -2
y = -2 - 2 = -4
Coordinates of P are (-2,-4)
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Recall tangent means 1 repeated root. Hence recall the condition for b^2-4ac when there is one repeated root.
Date Posted:
4 years ago
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