Question

Supply the number so that the quadratic equation below has 6 and 8 as it’s solutions.

x² - 14x +______ = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the number to complete the quadratic equation, we can use the fact that the sum of the solutions of a quadratic equation in the form of ax² + bx + c = 0 is equal to -b/a.

In this case, the sum of the solutions is 6 + 8 = 14.

So, the missing number that completes the quadratic equation is -14. The quadratic equation becomes:

x² - 14x + (-14) = 0

Answer 2

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

To find the missing number in the quadratic equation, we can start by using the fact that the solutions of the quadratic equation are given by the formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

In the equation x² - 14x + ______ = 0, the coefficient of the x² term is 1 (since it is written as x²), the coefficient of the x term is -14, and the constant term is the missing number. We can plug in the known values for the solutions, which are 6 and 8, and use the fact that the solutions are equal to x:

6 = (-(-14) ± sqrt((-14)^2 - 4(1)(______))) / (2(1))
8 = (-(-14) ± sqrt((-14)^2 - 4(1)(______))) / (2(1))

Simplifying these equations, we get:

6 = (14 ± sqrt(196 - 4(1)(______))) / 2
8 = (14 ± sqrt(196 - 4(1)(______))) / 2

To find the missing number, we need to solve for it. Let's solve the first equation for the missing number:

6 = (14 ± sqrt(196 - 4(1)(______))) / 2
Multiply both sides by 2:
12 = 14 ± sqrt(196 - 4(1)(______))
Subtract 14 from both sides:
-2 = ± sqrt(196 - 4(1)(______))
Square both sides to remove the square root:
(-2)^2 = (sqrt(196 - 4(1)(______)))^2
4 = 196 - 4(1)(______)
Simplify:
4 = 196 - 4(______)
4 = 196 - 4(______)
4 = 196 - 4______
4 = 196 - ______
4 = 196 - ______
Subtract 196 from both sides:
-192 = -______

Therefore, the missing number is 192. So, the quadratic equation is:

x² - 14x + 192 = 0

Answer 3

[AI-generated answer — Explain Bot]

To find the missing number in the quadratic equation, we can use the fact that the sum of the solutions of a quadratic equation is equal to the negation of the coefficient of the linear term (x) divided by the coefficient of the quadratic term (x²).

In the given equation, the sum of the solutions is known to be 6 + 8 = 14. Therefore, the missing number can be calculated as follows:

Sum of solutions = -b/a

In the equation x² - 14x + ______ = 0, the coefficient of the quadratic term (a) is 1, and the coefficient of the linear term (b) is -14. We need to find the missing number (-14) divided by the coefficient of the quadratic term:

-14/1 = -14

Thus, the missing number is -14.

Therefore, the complete quadratic equation becomes:

x² - 14x - 14 = 0