Juying Secondary School

JUYING SECONDARY SCHOOL

MATHEMATICS DEPARTMENT

ADDITIONAL MATHEMATICS

SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

Name: ______( ___ ) Class: ______Date: ______

Roots of Quadratic Equations (Revision Worksheet 1)

1. If the quadratic equation has 2 real and distinct roots, given that m is a constant, determine the range of values of m.

2. Find the range of values of p for which is always negative.

3. Find the range of values of k for which x2 + k(x + 2) + 3(x + 1) > 0 for all real values of x.

4. Show that the roots of the equation are real for all values of q.

5. Find the value of k for which the line y + 3x = k is a tangent to the curve

y = x2 + 5.

6. Find the range of values of m for which the equation has two real roots.

7. Show that the solutions of the equation are real for all real values of k.

8. The curve lies entirely above the line y + 3x = 2. Find the range of values of k.

9. Find the range of values of p for which meets the x-axis.

10. Find the range of values of p for which the line does not intersect the curve .

11. Determine whether the straight line is a tangent to the curve where a > 0.

12. The roots of the equation are real and distinct. Find the range of values of p.

13. Prove that the curve will always meet the line for all real values of m and n.

14. Find the range of values of k for which (x2 + 1) + (k + 1)x + (2k + 1) is never negative.

15. The quadratic equation has equal roots. Express k in terms of a and b.

Answers:

1.

2.

3.

5.

6.

8.

9.

10.

11. not a tangent

12.

14.

15.