Line meeting a curve with a constant in the x-squared term
Line meeting a curve with a constant in the x-squared term
Secondary 3
The equation of a curve is \(y=px^2+(p+2)x+2\), where \(p\) is a constant.
- Show that the line \(y=1-x\) meets the curve for all real values of \(p\).
- State the number of points at which the line meets the curve when \(p=0\), and explain why.
Solution:
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Answer:(a) Shown: \(p\ne0\) gives \(D=(p+1)^2+8>0\); \(p=0\) gives \(x=-\dfrac13\). (b) One point: the equation is linear when \(p=0\).
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