Question

Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation. Provide a unique example to back up your explanation.

Answer 1

when the discriminant is greater than zero D>0 there are two real solutions differents
- when D=0 there are two solutions equales
- when D<0 there are two solutions complex

Answer 2

1. \[x ^{2} +4x +3 =0\]

Answer 3

D=16-12=4
x_1,_2=(-4+/-sqrt(4))/2=(-4+/-2)/2= -3 and -1

Answer 4

2.

Answer 5

\[x ^{2}+2x+1=0\]

Answer 6

D=4-4=0
x_1,_2=(-2+/- 0)/2= -2/2 =-1

Answer 7

3.

Answer 8

\[x ^{2}-x+1=0\]

Answer 9

D=1-4= -3
x_1,_2=(1+/- sqrt(-3))/2 = (1+/- (i)sqrt(3))/2