Question

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

x^2 - 14x +______ = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the missing number, we can use the fact that the sum of the solutions of a quadratic equation is given by the negative coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the solutions is -14.

We are given that the solutions are 6 and 8. Therefore, we can calculate the sum of the solutions:

6 + 8 = 14

Since the sum of the solutions is -14, we can set up the equation:

14 + x = -14

Solving for x, we find:

x = -14 - 14
x = -28

Therefore, the missing number is -28.

The quadratic equation with solutions 6 and 8 is:

x^2 - 14x - 28 = 0

Answer 2

That's not right

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect answer. Let's solve the problem correctly.

We are given that the solutions of the quadratic equation are 6 and 8. Solutions of a quadratic equation can also be referred to as the roots. Let's denote the missing number as "a".

For a quadratic equation in the form ax^2 + bx + c = 0, the sum of the roots is given by the equation:

sum_of_roots = -b/a

In this case, the sum of the roots is 6 + 8 = 14. So we have:

14 = -(-14)/a

Simplifying the equation:

14 = 14/a

To solve for "a", we can multiply both sides by "a":

14a = 14

Dividing both sides by 14:

a = 1

Therefore, the missing number is 1.

The quadratic equation with solutions 6 and 8 is:

x^2 - 14x + 1 = 0

Answer 4

thats not right either

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies once again for the incorrect answer. Let's solve the problem correctly this time.

We are given that the solutions of the quadratic equation are 6 and 8. The quadratic equation can be written in the form:

(x - r1)(x - r2) = 0

Where r1 and r2 are the roots/solutions of the equation. Substituting the given values of 6 and 8, we have:

(x - 6)(x - 8) = 0

Expanding the equation, we get:

x^2 - 14x + 48 = 0

Therefore, the missing number in the original equation x^2 - 14x + ______ = 0 is 48.