Hint
Use the stated units and precision. Factor the quadratic completely, set each factor to zero and retain both roots.
Worked solution
(a)
\(\left(x + 2\right) \left(4 x - 5\right)\) expands to the given polynomial. The zero-product rule gives \(4x-5=0\) or \(x+2=0\).
Answer: \(\left(x + 2\right) \left(4 x - 5\right)\); \(\displaystyle x=\frac{5}{4}\text{ or }x=-2\)
(b)
Factor the quadratic completely, set each factor to zero and retain both roots.
\(-2\)
Answer: \(-2\)
(c)
Factor the quadratic completely, set each factor to zero and retain both roots.
\(-10\)
Answer: \(-10\)
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: Find the two complete linear factors, including any nonunit leading coefficient.
- 1 mark: Set each factor to zero and solve both linear equations.
- 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: Factor the quadratic completely, set each factor to zero and retain both 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: Factor the quadratic completely, set each factor to zero and retain both 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: Keep intermediate values exact until the final step.
Total: 7 marks.