Question

in 4x2 -3x+x/24 findthe sum of coffcens of variable​ ​

Answer 1

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (22x2 -  20x) -  24  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4x2 - 20x - 24  =   4 • (x2 - 5x - 6)  

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 5x - 6  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    x2 - 6x + 1x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-6)

            Which is the desired factorization

Equation at the end of step

3

:

 4 • (x + 1) • (x - 6)  = 0  

STEP

4

:

Theory - Roots of a product

4.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Equations which are never true:

4.2      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Solving a Single Variable Equation:

4.4      Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

Supplement : Solving Quadratic Equation Directly

Solving    x2-5x-6  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Step-by-step explanation:

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