a. find the value of the discriminant

b. describe the number and type of root
c. find the exact solution by using quadratic formula

1. p^2+12p=-4
2. 9x^2-6x+1=0
3. 2x^2-7x-4=0

3 answers

2. 9x^2-6x+1=0
b^2-4ac=-6^2-4(9)(1) or 0
so it has 1 rational root.
p^2 + 12 p + 4 = 0

b^2-4ac = 144 -16 = 128

positive
so there will be two real roots

[ -12 +/- sqrt(128) ] / 2
2.

36 -4(9) = 36 -36 = 0
so
repeated real root

[ 6 +/- 0 ] / 18 = 1/3 and 1/3 (same, parabola just touches the x axis)