DP Mathematics HL Questionbank

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Directly related questions

• 18M.2.hl.TZ2.10d.ii: Show that \(\alpha \) + β < −2.
• 18M.2.hl.TZ2.10d.i: Find \(\alpha \) and β in terms of \(k\).
• 18M.2.hl.TZ1.2: The equation \({x^2} - 5x - 7 = 0\) has roots \(\alpha \) and \(\beta \). The equation...
• 16M.2.hl.TZ2.12b: (i)     By forming a quadratic equation in \({{\text{e}}^x}\), solve the equation \(h(x) = k\),...
• 16M.2.hl.TZ1.11a: Find the solutions of \(f(x) > 0\).
• 16N.2.hl.TZ0.11c: Deduce that...
• 16N.2.hl.TZ0.11b: Find the values of the constants \(a\) and \(b\).
• 16N.1.hl.TZ0.5: The quadratic equation \({x^2} - 2kx + (k - 1) = 0\) has roots \(\alpha \) and \(\beta \) such...
• 17N.2.hl.TZ0.7: In the quadratic equation \(7{x^2} - 8x + p = 0,{\text{ }}(p \in \mathbb{Q})\), one root is three...
• SPNone.1.hl.TZ0.2a: Write down the numerical value of the sum and of the product of the roots of this equation.
• 14M.1.hl.TZ1.4: The equation \(5{x^3} + 48{x^2} + 100x + 2 = a\) has roots \({r_1}\), \({r_2}\) and...
• 14M.1.hl.TZ2.4: The roots of a quadratic equation \(2{x^2} + 4x - 1 = 0\) are \(\alpha \) and \(\beta...
• 15M.1.hl.TZ1.7a: For the polynomial equation \(p(x) = 0\), state (i)     the sum of the roots; (ii)     the...
• 15M.1.hl.TZ1.7b: A new polynomial is defined by \(q(x) = p(x + 4)\). Find the sum of the roots of the equation...
• 15M.1.hl.TZ2.12b: It is now given that \(p =  - 6\) and \(q = 18\) for parts (b) and (c) below. (i)     In the...
• 15M.1.hl.TZ2.12a: (i)     \(p =  - (\alpha  + \beta  + \gamma )\); (ii)    ...
• 15M.1.hl.TZ2.12c: In another case the three roots \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \) form a geometric...
• 15N.1.hl.TZ0.10b: the value of \({a_0}\).
• 15N.1.hl.TZ0.10a: the degree of the polynomial;
• 14N.1.hl.TZ0.2b: Another quadratic equation \({x^2} + px + q = 0,{\text{ }}p,{\text{ }}q \in \mathbb{Z}\) has...
• 14N.1.hl.TZ0.2a: Without solving the equation, find the value of (i)     \(\alpha  + \beta \); (ii)    ...