4. (a) If –2 is a root of the quadratic equation k x 2 – 4x – 2 = 0, fi nd k ∈ R.
(b) Show that 1 + √
__ 2 is a solution of the
equation x 2 – 2x – 1 = 0.
(c) Investigate if – 3 _
2 is a solution of the equation 2 x 2 + 5x + 3 = 0. –1 5 x 105 (b) y
5. Solve the following by using the quadratic formula, giving your answers as a rational or in surd form and then as decimals, correct to two decimal places:
(a) x 2 – 2x – 30 = 0 (b) x 2 = 2x + 9 (c) 4 x 2 – 19x + 1 = 0 (d) 6 x 2 + x – 2 = 0 (e) 6 x 2 – 15x – 18 = 0 (f) 3 x 2 – 8x – 2 = 0 (g) 7 x 2 + 8x = 2 (h) (3x – 2)(2x + 4) – 4 x 2 + 5 = 0 (i) x 2 – 3 = 0 (j) 4 x 2 – 32 = 0
6. The graph of y = a x 2 + bx + c is shown. State how many real roots there are of the equation a x 2 + bx + c = 0 and read them off from the graph. Check your answers.
