Step-by-step explanation:
For a quadratic expression ax²+bx + c = 0
The discriminant D = b²-4ac
Given the following quadratic equation;
x^2 - 6x-27 = 0
a = 1, b = -6, c = -27
D = (-6)²-4(-27)
D = 36+108
D = 144
Hence the discriminant is 144
For the roots;
x = -b±√D/2a
x = 6±√144/2
x = 6±12/2
x = 18/2 and -6/2
x = 9 and -3
For the expression x2 - 25 = 0
a = 1, b = 0 and c = -25
D = (0)²-4(-25)
D = 100
Hence the discriminant is 100
For the roots;
x = 0±√100/2
x = ±10/2
x = ±5
x =-5 and 5
Given the following quadratic equation;
x^2 +10x+25 = 0
a = 1, b = 10, c = 25
D = (10)²-4(25)
D = 100-100
D = 0
Hence the discriminant is 0
For the roots
x = -10±√0/2
x = -10/2
x = -5
Given the following quadratic equation;
2x^2 - 5x+3 = 0
a = 2, b = -5, c = 3
D = (-5)²-4(2)(3)
D = 25-24
D = 1
Hence the discriminant is 1
For the roots;
x = 5±√1/2(2)
x = 5±1/4
x = 5+1/4 and 5-1/4
x = 6/4 and 4/4
x = 3/2 and 1
x = 18/2 and -6/2
x = 9 and -3
