Question

What is the lesser and greater x of 4x^2 40x 84=0

Answer 1

The lesser value of x is -7, and the greater value of x is -3, which are the solutions to the quadratic equation 4x^2 + 40x + 84 = 0

Explanation:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a = 4, b = 40, and c = 84 in this equation.

Calculate the discriminant (the value inside the square root) first:

Discriminant = b^2 - 4ac = (40)^2 - 4 * 4 * 84 = 1600 - 1344 = 256.

Now, apply the quadratic formula to find the solutions for x:

x = (-40 ± √256) / (2 * 4) = (-40 ± 16) / 8.

Now, calculate the two possible values for x:

x1 = (-40 + 16) / 8 = -24 / 8 = -3.

x2 = (-40 - 16) / 8 = -56 / 8 = -7.

So, the lesser value of x is -7, and the greater value of x is -3, which are the solutions to the quadratic equation 4x^2 + 40x + 84 = 0.

Answer 2

The lesser value of x is -7, and the greater value of x is -3.

Explanation:

To find the lesser and greater values of x for the equation 4x^2 + 40x + 84 = 0, we can use the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, the equation is in the form of ax^2 + bx + c = 0, with a = 4, b = 40, and c = 84.

Using the quadratic formula, we can substitute these values and calculate the roots:

x = (-40 ± √(40^2 - 4 * 4 * 84)) / (2 * 4)

Simplifying further:

x = (-40 ± √(1600 - 1344)) / 8

x = (-40 ± √256) / 8

x = (-40 ± 16) / 8

We have two possible values for x:

1. When we add the square root:

x = (-40 + 16) / 8

x = -24 / 8

x = -3

2. When we subtract the square root:

x = (-40 - 16) / 8

x = -56 / 8

x = -7

So, the lesser value of x is -7, and the greater value of x is -3.