Hint
Use the stated units and precision. Use the signed coefficients in the quadratic formula or completed-square form.
Worked solution
(a)
\(b^2-4ac=36\) is positive. Substitution in the quadratic formula gives \(-4\), \(2\). Each satisfies the original equation.
Answer: \(\left\{-4, 2\right\}\)
(b)
Evaluate the exact roots \(-4\), \(2\) before rounding each final value to three significant figures.
Answer: \(-4.00\), \(2.00\)
(c)
Use the signed coefficients in the quadratic formula or completed-square form.
\(-8\)
Answer: \(-8\)
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) · 3 marks
- 1 mark: Substitute all signed coefficients into the complete quadratic formula.
- 1 mark: Retain both roots and simplify exact square roots where possible.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
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: Evaluate both exact branches with guard digits and round only at the end.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
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: Use the signed coefficients in the quadratic formula or completed-square form.
- 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: 7 marks.