Graphical view of polynomial equations Problem set B Answers

1. (a) \(x = −3.24, 1.00, 1.24\)
2. (b) \(x = 1\); the graph touches the \(x\)-axis there and turns back

\(x = −1.13, 0.798, 3.33\)

\(y = (x − 5)^2 + 0\); vertex \((5, 0)\); \(x = 5\)

1. (a) 1 different real root
2. (b) 2 different real roots
3. (c) 3 different real roots

\(t = 0.309, 4.51, 7.18\)

1. (a) \(a = 2\): 0; \(a = 3\): 1; \(a = 4\): 0
2. (b) A cubic goes from far below to far above the axis, so it must cross it. A quartic has both ends up, so it can sit above the axis.

1. (a) \(−27 < k < 5\)
2. (b) \(k = −27\) or \(k = 5\)

1. (a) \(k = 9\); \(x = −3\)
2. (b) 0 real roots