Question

PLEASE HELP WITH THE FIRST 3 parts

Answer 1

Answer:

a) x = -2+√3 and -2-√3

b) x = -1 + 2√3/3 and -1 - 2√3/3

c) x = 3.185 and 0.315

Step-by-step explanation:

To solve the following quadratic equation, we will use the general formula

x = -b±√b²-4ac/2a

a) x²+4x+1 = 0

a = 1, b = 4 and c = 1

Substitute into the formula

x = -4±√4²-4(1)(1)/2(1)

x = -4±√16-4/2

x = -4±√12/2

x = -4±2√3/2

x  = (-4+2√3)/2 and  (-4-2√3)/2

x = -2+√3 and -2-√3

b) 3x²+6x-1 = 0

a = 3, b = 6 and c = -1

Substitute into the formula

x = -6±√6²-4(3)(-1)/2(3)

x = -6±√36+12/6

x = -6±√48/6

x = -6±4√3/6

x  = (-6+4√3)/6 and  (-6-4√3)/6

x = -1 + 2√3/3 and -1 - 2√3/3

c) 2x² - 7x + 2 = 0

a = 2, b = -7 and c = 2

x = -(-7)±√(-7)²-4(2)(2)/2(2)

x = 7±√49-16/4

x =7±√33/4

x = 7±5.74/4

x = 7+5.74/4 and 7-5.74/4

x = 12.74/4 and 1.26/4

x = 3.185 and 0.315