The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?

Question

i hate the quadratic formula please help

Answer 1

"In elementary algebra, a quadratic equation is any equation having the form where x represents an unknown, and a, b, and c represent numbers such that a is not equal to 0." -- Wikipedia  [note: bold added]

 

A solution is a value for x that makes an equation true.  Therefore, solutions x=2 and x=7 make this equation true:

     ax² + bx + c = 0

 

"The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two. Quadratic equations can be solved by factoring, by completing the square, by using the quadratic formula, or by graphing."  -- same Wikipedia  [note: bold added]

 

There may be two solutions to a quadratic equation.  These are indicated by the +/- of the quadratic formula.

 

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The problem gives the solutions as x=2 and x=7.  Using the format of the problem equation that results from factoring:

      (x - 2)(x - 7) = 0   

    [note that the multiplicative property of 0 means that at least one expression must be equal to 0)

 

Now, the quadratic formula is:

     x = (-b  ± √(b²-4ac) ) / 2a

   which results in solutions:

     x=2   or   x=7     for this problem

 

You must now go to "the following" and determine which expression involving the nonzero constant k equals:

      (x-2)(x-7)=0= <expression involving k>

Answer 2

1) x = 2 and x = 7 are not solutions. They are factors of the polynomial equal to zero.

2) If x = 2 and x = 7 are factors of the polynomial equation, the -2 and -7 are solutions.

3) You do not give "the following."