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Quadratics - the Discriminant - advanced applications.

Test Yourself 1.

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Answer the following questions - you will need to use the discriminant:

Identification of tangents etc. | 1. | |

2. | ||

3. Given that the line lx + my + n = 0 is a tangent to
x |
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4. | ||

5. A parabola whose equation is y = kx^{2} (where k is a constant) has the line y = -6x + 3 as a tangent.
Answer.(i) kx ^{2} + 6x - 3 = 0(ii) k = -3 (iii) Point of contact (1, -3). |
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6 | ||

Nature of roots. | 15. Show that the constants k and l have different signs if the quadratic equation
has no real roots . | |

16. (i) For what values of k does the quadratic equation
kx have real roots?
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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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