Easy -1.2 This is a straightforward application of the conjugate root theorem for quadratics with real coefficients. Students need only recall that complex roots come in conjugate pairs, then use sum and product of roots to find a and b. It's a standard textbook exercise requiring minimal problem-solving, though the Further Maths context places it slightly above the easiest recall questions.
3 One root of the quadratic equation \(x ^ { 2 } + a x + b = 0\), where \(a\) and \(b\) are real, is the complex number \(4 - 3 \mathrm { i }\). Find the values of \(a\) and \(b\).
3 One root of the quadratic equation $x ^ { 2 } + a x + b = 0$, where $a$ and $b$ are real, is the complex number $4 - 3 \mathrm { i }$. Find the values of $a$ and $b$.
\hfill \mbox{\textit{OCR FP1 2012 Q3 [4]}}