3.  This is the part of the equation under the radical sign. (b 2 – 4ac)  When that is positive, there will be two answers.  When that is negative, there will be no real solution.  When that is zero, there will be one answer.

4.  2x 2 + 4x + 3 = 0  a = 2; b = 4; c = 3  b 2 – 4ac  (4) 2 – (4)(2)(3)  16 – 24= -8  The answer is negative, so there are no real solutions.

5.  2x 2 – 11x + 6 = 0  a = 2; b = -11; c = 6  b 2 – 4ac  (-11) 2 – (4)(2)(6)  121 – 48= 73  The answer is positive, so there are two real solutions.

6.  2x 2 + 12x = -18  2x 2 + 12x + 18 = 0  a = 2; b = 12; c = 18  b 2 – 4ac  (12) 2 – (4)(2)(18)  144 – 1444= 0  The answer is zero, so there is one real solution.

7.  A weight 1 foot above the ground on a carnival strength test is shot straight up with an initial velocity of 35 feet per second. Will it ring the bell at the top (20 feet high)? Use the discriminant to explain your answer.  h = -16t 2 + vt + c  h is the height, v is the initial velocity and c is the weight of the weight.  20 = -16t 2 + 35t + 1  0 = -16t 2 + 35t - 19

8.  -16x 2 + 35x - 19 = 0  a = -16; b = 35; c = -19  b 2 – 4ac  (35) 2 – (4)(-16)(-19)  1235 – 1216 = 19  The answer is positive, so there are two real solutions.  So, the weight will reach a height of 20 feet and ring the bell.

9.  3x + 2x 2 + 6 = 0  3x 2 = 13x – 4  9x 2 + 16 = -24x  0 solutions  2 solutions  1 solution