FP1.1.6 - Finding conjugate complex roots

Finding conjugate complex roots For example, and/or real roots of a quartic (i) f(x) = x4 − x3 − 5x2 + 7x + 10 equation with real coefficients.; Given that x = 2 + i is a root of f(x) = 0, use algebra to find the three other roots of f(x) = 0 (ii) g(x) = x4 − x3 + 6x2 + 14x − 20 Given g(1) = 0 and g(−2) = 0, use algebra to solve g(x) = 0 completely.

Use fp1.1.6 - finding conjugate complex roots to connect the rule to the data and decision in the question.

This matters because fp1.1.6 - finding conjugate complex roots determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.1.6 - finding conjugate complex roots to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP1.1.6 - Finding conjugate complex roots is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.