Question

find the the equation that formed by cubing each root of the equation x²-5x+6=0
​

Answer 1

Step-by-step explanation:

In a quadratic in the form

a

x

2

+

b

x

+

c

, find two numbers that multiply to

a

⋅

c

and add up to

b

in order to factor.

In this case, we need two numbers that multiply to

6

and add up to

−

5

. These two numbers are

−

2

and

−

3

.

Now, split up the

x

term into these two numbers. Next, factor the first two terms and the last two terms separately, then combine them. Lastly, set each factor equal to zero and solve for

x

in each one. Here's what all that looks like:

x

2

−

5

x

+

6

=

0

x

2

−

2

x

−

3

x

+

6

=

0

x

(

x

−

2

)

−

3

x

+

6

=

0

x

(

x

−

2

)

−

3

(

x

−

2

)

=

0

(

x

−

3

)

(

x

−

2

)

=

0

x

−

3

=

0

x

−

2

=

0

x

=

3

x

=

2

These are the two solutions. Hope this helped!

Answer 2

X^2-5x+6=0
Factors of -5x are -2x,-3x
X^2 -2x -3x+6=0(replacing-5x with its factors)
X(x-2) -3(x-2)=0
(X-2)(x-3)=0
X-2=0. X-3=0
X=2. X=3
Therefore the two solutions for the given equation are 2,3