Dr. J's Maths.com

**Where the techniques of Maths**

are explained in simple terms.

are explained in simple terms.

Quadratics - the Discriminant - advanced applications.

Test Yourself 1 - Solutions.

- Algebra & Number
- Calculus
- Financial Maths
- Functions & Quadratics
- Geometry
- Measurement
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- Probability & Statistics
- Trigonometry
- Maths & beyond
- Index

Identification of tangents etc. | 1. | ||||

2. | |||||

3. | |||||

4. (i) Show that for all values of m, the line y = mx - 3m^{2} touches the parabola x^{2} = 12y.
(ii) Find the values of m for which this line passes through the point (5,2). (iii) Hence determine the equations of the two tangents to the given parabola from the point (5,2). |
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5.Consider the line y = 6x - k and the parabola | |||||

6. | |||||

More advanced. | 7.Show that the constants k and l have different signs if the quadratic equation has no real roots ( ). 16. Increasing fn |
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8. Show that the quadratic equation (a has real and rational roots for all values of x if a, b and c are rational. |
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