The equation of a curve is $$\(y=\frac{1}{2} k^{2} x^{2}-2 k x+2\)$$ and the equation of a line is $$\(y=k x+p\)$$, where $$\(k\)$$ and $$\(p\)$$ are constants with $$\(0< k< 1\)$$. It is given instead that the line and the curve do not intersect. Find the set of possible values of $$\(p\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_w24_qp_12 Year:2024 Question No:9(b)

Answer:



Knowledge points:

1.1.2 find the discriminant of a quadratic polynomial and use the discriminant
1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)

Solution:

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