Algebra 2 Discriminant Problems Solve for C

Question

Find the values or intervals of k for which each of the following has for:

3x²-6x-k=0

1. two non equal real roots
2. two imaginary roots

2x^2+4x+k

1. two non equal real roots
2. two imaginary roots

Answer 1

3x^2 -6x - k = 0

the discriminate is b^2 - 4ac

where ax^2 + bx + c = 0

in this problem a = 3, b =-6 and c = k

the solutions are both real if the discriminate > or = 0

the discriminate = 36+12k

36+12k > or = 0 when

k> or = -3

they're nonequal real roots when k>-3. They're equal real roots if k=-3

the solutions are both imaginary if k<-3

2x^2 + 2x + k = 0

has a discriminate = 4-8k. It's >0 when k< 1/2. IF k<1/2, there are 2 nonequal real roots

IF k>1/2 there are two unequal imaginary roots