Respuesta :

altavistard

Answer:

the "negative solution" is -3

Step-by-step explanation:

Represent the number by n.

Then n^2 - 24 = 5n

We rewrite this in standard quadratic form:

n^2 - 5n - 24 = 0

This factors as follows;  (n + 3)(n - 8) = 0

The roots are n = -3 and n = 8.  Thus, the "negative solution" is -3

vijayhalder031

The correct answer is -3

What is quadratic equation?

The equation having the highest degree 2 of a variable is known as quadratic equation.

How to find the roots of the quadratic equation?

The roots of the equation can be find by following steps

  • The roots of the equation can be found by splitting the middle term.
  • Take the product of the coefficient of the first term and the last term
  • Split the middle term by sum of the product.
  • After splitting the middle term the equation will have 4 terms and then take the common factors.
  • Find the two root.

How to solve the problem?

Let us assume the number to be x

So, According to the statement

the difference of the square of the number and 24  is [tex]x^{2}-24[/tex]

is equal to 5 times that number is [tex]5x[/tex]

So the equation will be [tex]x^{2} -24=5x\\[/tex]

Therefore ,

[tex]x^{2} -5x-24=0\\x^{2} +3x-8x-24=0\\\x(x+3)-8(x+3)=0\\(x+3)(x-8)=0[/tex]

Therefore , x = -3 or x = 8

Hence the negative solution is -3

Learn more about splitting the middle term below

https://brainly.in/question/17570015

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