DP Mathematics HL Questionbank

• Syllabus

1.8

Sub sections and their related questions

Conjugate roots of polynomial equations with real coefficients.

• 09M.1.hl.TZ2.7: Given that \({z_1} = 2\) and \({z_2} = 1 + \sqrt 3 {\text{i}}\) are roots of the cubic equation...
• 10N.2.hl.TZ0.6: Consider the polynomial \(p(x) = {x^4} + a{x^3} + b{x^2} + cx + d\), where a, b, c, d...
• 09N.2.hl.TZ0.7: (a) the other two roots; (b) \(a\) , \(b\) and \(c\) .
• 09M.2.hl.TZ1.2: (a)     Show that the complex number i is a root of the...
• 14M.2.hl.TZ1.1: One root of the equation \({x^2} + ax + b = 0\) is \(2 + 3{\text{i}}\) where...
• 14M.2.hl.TZ2.13e: Given that \(u\) and \(v\) are roots of the equation \({z^4} + b{z^3} + c{z^2} + dz + e = 0\),...
• 16M.2.hl.TZ1.9a: Write down the other two roots in terms of \(c\) and \(d\).
• 16M.2.hl.TZ1.9b: Find the value of \(c\) and the value of \(d\).
• 16M.1.hl.TZ2.12d: (i)     Given that \(\alpha  = w + {w^2} + {w^4}\), show that...
• 16M.1.hl.TZ2.12e: Using the values for \(b\) and \(c\) obtained in part (d)(ii), find the imaginary part of...
• 16M.1.hl.TZ1.12c: Find an expression in terms of \(\theta \) for...
• 16M.1.hl.TZ1.12d: (i)     Show that \(zz{\text{*}} = 1\). (ii)     Write down the binomial expansion of...
• 16M.1.hl.TZ1.12e: Hence solve \(4{\cos ^3}\theta  - 2{\cos ^2}\theta  - 3\cos \theta  + 1 = 0\) for...