Equation 3 + x = 24 / ( x + 1 ) is a quadratic equation ?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

(3+x) = 24/(x+1)

First w need to rewrite th equations. We will get rid of the fraction by multiplying the equation by the denominator.

Let us multuply by (x+1):

==>(3 +x)(x+1) = 24

==> Now open brackets:

=> (3x + 3 + x^2 + x = 24

Now,  combine like terms:

==> x^2 + 4x - 21 = 0

Then the equation is quadratic.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If it is written in the original form, it doesn't look like a quadratic equation, but it is.

We have to isolate x to the left side. For this reason, we'll have to multiply both sides by the denominator x+1.

(3 + x)(x + 1) = 24(x + 1)/ (x + 1)

We'll simplify and we'll get:

(3 + x)(x + 1) = 24

We'll remove the brackets:

3x + 3 + x^2 + x - 24 = 0

We'll combine like terms:

x^2 + 4x - 21 = 0

Since the maximum order of the equation is 2, the equation is a quadratic.

 The number of the roots is 2 and the formula for finding the roots is:

x1 = [-b+sqrt(b^2 - 4ac)]/2a

x2 = [-b-sqrt(b^2 - 4ac)]/2a

Let's identify a,b,c:

a = 1

b = 4

c = -21

x1 = [-4+sqrt(16+84)]/2

x1 = (-4+10)/2

x1 = 3

x2 =  (-4-10)/2

x2 = -7

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The given equation 3+x = 24/(x+1) is not a quadratic equation.

A quadratic equation is a second degree polynomial with positive integral powers with real coefficients.

So the given equation is not a quadratic equation, as in ivolves  with the negative powers of (x+1) on the right side: 24(x+1)^(-1).

The given equation could be converted into a quadratic equation by multiplying both sides by (x+1):

(3+x)(x+1) = 24 is a 2nd degree polymial equation

3x+3+x^2+3 = 24 is a 2nd degree polynomial equation

x^2+4x+3-24 = 0 is a second degree polynomial equation.

So any second degree polynomial equation is a quadratic equation.

In all these a cannot be zero. b oe c can be zero.

x^2+4x-21 = 0.

So (x-7)(x+3) = 0.

x-7 = 0. x+3 = 0.

x= 7. and x=-3.

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