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Problems

  1. Assume that 0 is a solution to the quadratic equation \((k+4)x^2+3x+k^2+3k-4=0\) of x. What is \(k\)?

  2. Assume that \(m, n\) are the solutions to the quadratic equation \(x^2 - 3x -5 =0\). What is \(m^2 + 2n^2 - 3n\) without explicitly solving the equation?

  3. In Figure 1, \(AB=AC\), \(\angle A = 120^{\circ}\), \(MN\perp AB\), \(AN=NB\). Prove \(CM=2BM\).


Figure 1: Figure 1

  1. In Figure 2, \(AB=AC\), \(AD = BC = CE = DE\). Prove \(\angle BAC=100^{\circ}\).


Figure 2: Figure 2

Hints


\(\beta + \gamma = 60^{\circ}\)

Solutions

  1. \(k=1\)

  2. \(24\)

Set1