Task 2 Equation

a

b

Discriminant

Nature of the

Roots

x2 - 6x-27 = 0

x2 - 25 - 0

x2 + 10x + 25 - 0

2x2 - 5x + 3 = 0

HELP PLEASEE

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