Question

What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?

a x = the quantity of 5 plus or minus the square root of 29 all over 2
b x = the quantity of negative 5 plus or minus the square root of 29 all over 2
c x = the quantity of 5 plus or minus the square root of 21 all over 2
d x = the quantity of negative 5 plus or minus the square root of 21 all over 2

Answer 1

The correct answer is (a) x = (5 ± √29) / 2.

To find the solutions of the quadratic equation x^2 - 5x - 1 = 0 using the quadratic formula, we can identify the values of a, b, and c:

a = 1

b = -5

c = -1

Plugging these values into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c:

x = (-(-5) ± √((-5)^2 - 4(1)(-1))) / (2(1))

x = (5 ± √(25 + 4)) / 2

x = (5 ± √29) / 2

Therefore, the solutions to the equation x^2 - 5x - 1 = 0 are x = (5 + √29) / 2 and x = (5 - √29) / 2, which corresponds to option (a).

Answer 2

a

Explanation:

The explanation is attached below.