Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Quadratics - the Discriminant - advanced applications.
Test Yourself 1 - Solutions.


 

 

Identification of tangents etc. 1.
  2.
  3.

  4. (i) Show that for all values of m, the line y = mx - 3m2 touches the parabola x2 = 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).
  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 Eqn 15
has no real roots ( Eqn 15B). 16. Increasing fn
 

8. Show that the quadratic equation

(a2 - b2)x2 + 2b(a - c)x + (b2 - c2) = 0

has real and rational roots for all values of x if a, b and c are rational.