THE DISCRIMINANT

THE QUADRATIC FORMULA

xb b ac

a

2 4

2

THE DISCRIMINANT

This is the part of the equation under the radical sign. (b2 – 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.

FIND THE NUMBER OF SOLUTIONS:

2x2 + 4x + 3 = 0 a = 2; b = 4; c = 3 b2 – 4ac (4)2 – (4)(2)(3) 16 – 24= -8 The answer is negative, so there are no

real solutions.

FIND THE NUMBER OF SOLUTIONS:

2x2 – 11x + 6 = 0 a = 2; b = -11; c = 6 b2 – 4ac (-11)2 – (4)(2)(6) 121 – 48= 73 The answer is positive, so there are two

real solutions.

FIND THE NUMBER OF SOLUTIONS:

2x2 + 12x = -18 2x2 + 12x + 18 = 0 a = 2; b = 12; c = 18 b2 – 4ac (12)2 – (4)(2)(18) 144 – 1444= 0 The answer is zero, so there is one real

solution.

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 = -16t2 + vt + c h is the height, v is the initial velocity and c

is the weight of the weight. 20 = -16t2 + 35t + 1 0 = -16t2 + 35t - 19

-16x2 + 35x - 19 = 0 a = -16; b = 35; c = -19 b2 – 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.

TRY THESE…

3x + 2x2 + 6 = 0

3x2 = 13x – 4 9x2 + 16 = -24x

0 solutions 2 solutions 1 solution