Moderate -0.8 This is a straightforward Further Maths question requiring routine application of the quadratic formula to find complex roots, then converting to modulus-argument form using standard formulas. While it involves multiple steps, each is a direct application of learned techniques with no problem-solving insight required, making it easier than average even for Further Maths.
2 Find the roots of the quadratic equation \(x ^ { 2 } - 8 x + 17 = 0\) in the form \(a + b \mathrm { j }\).
Express these roots in modulus-argument form.
M1 for use of quadratic formula. A1 both roots correct
\(\sqrt{17}(\cos 0.245 + j\sin 0.245)\)
M1
Attempt to find modulus and argument
\(\sqrt{17}(\cos 0.245 - j\sin 0.245)\)
F1, F1 [3]
One mark for each root. Accept \((r,\theta)\) form. Allow any correct arguments in radians or degrees, including negatives: \(6.04,\ 14.0°,\ 346°\). Accuracy at least 2 s.f. S.C. F1 for consistent use of their incorrect modulus or argument (not both, F0)
## Question 2:
$4-j,\ 4+j$ | M1, A1 **[2]** | M1 for use of quadratic formula. A1 both roots correct
$\sqrt{17}(\cos 0.245 + j\sin 0.245)$ | M1 | Attempt to find modulus and argument
$\sqrt{17}(\cos 0.245 - j\sin 0.245)$ | F1, F1 **[3]** | One mark for each root. Accept $(r,\theta)$ form. Allow any correct arguments in radians or degrees, including negatives: $6.04,\ 14.0°,\ 346°$. Accuracy at least 2 s.f. S.C. F1 for consistent use of their incorrect modulus or argument (not both, F0)
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2 Find the roots of the quadratic equation $x ^ { 2 } - 8 x + 17 = 0$ in the form $a + b \mathrm { j }$.\\
Express these roots in modulus-argument form.
\hfill \mbox{\textit{OCR MEI FP1 2005 Q2 [5]}}