Hint
Use the stated units and precision. Set the given nonzero-root factors equal to zero.
Worked solution
(a)
Set the given nonzero-root factors equal to zero.
The factor \(x - 3\) is zero at 3.
Answer: \(3\)
(b)
Use the other linear factor and order the positive roots.
The factor \(x - 6\) is zero at 6.
Answer: \(6\)
(c)
Expand systematically and collect the first-power term.
The linear coefficient is \(54\) after multiplying all three brackets.
Answer: \(54\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Set the given nonzero-root factors equal to zero.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the other linear factor and order the positive roots.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Expand systematically and collect the first-power term.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.