Question

What are the solutions of the quadratic equation?

2x^2 – 16x + 32 = 0

Answer 1

[AI-generated answer — Step-by-Step Bot]

To find the solutions of a quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Given the equation 2x^2 - 16x + 32 = 0, we can identify the coefficients as follows:
a = 2
b = -16
c = 32

Now, let's substitute these values into the quadratic formula:

x = (-( -16) ± √((-16)^2 - 4 * 2 * 32)) / (2 * 2)

Simplifying:

x = (16 ± √(256 - 256)) / 4
x = (16 ± √(0)) / 4

Since the discriminant (√(b^2 - 4ac)) is zero, it means that there is only one solution. The solutions are:

x = 16/4
x = 4

Thus, the quadratic equation 2x^2 - 16x + 32 = 0 has one solution, which is x = 4.

Answer 2

[AI-generated answer — Bot GPT 3.5]

To find the solutions of the quadratic equation 2x^2 – 16x + 32 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation:
a = coefficient of x^2 term = 2
b = coefficient of x term = -16
c = constant term = 32

Plugging these values into the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4(2)(32))) / (2(2))
x = (16 ± √(256 - 256)) / 4
x = (16 ± √0) / 4

Since the discriminant (b^2 - 4ac) is equal to zero, the square root of zero is zero. Therefore, we have:

x = (16 ± 0) / 4
x = 16 / 4
x = 4

So the quadratic equation 2x^2 – 16x + 32 = 0 has only one solution, which is x = 4.

Answer 3

[AI-generated answer — Explain Bot]

To find the solutions of a quadratic equation, you can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the quadratic equation 2x^2 – 16x + 32 = 0, the values of a, b, and c are:

a = 2
b = -16
c = 32

Now, let's substitute these values into the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4 * 2 * 32)) / (2 * 2)

Simplifying further:

x = (16 ± √(256 - 256)) / 4
x = (16 ± √0) / 4

Since the square root of 0 is 0, we have:

x = (16 ± 0) / 4

Simplifying even further:

x = 16 / 4
x = 4

Hence, the quadratic equation 2x^2 – 16x + 32 = 0 has a single solution, which is x = 4.