Quadratic equation

Question

Write a quadratic equation having the given numbers as solutions.

-3 and -1

 

The quadratic equation is _=0

 

(Type your answer in standard form. Type an expression using x as a variable)

Answer 1

The Multiplicative Property of Zero (0*a=0) says that any value multiplied by zero results in zero.

 

So, if a*b = 0, then either a=0 or b=0 or both.

 

To "solve" an equation means to find the value(s) for which the equation is true.  In this case, the solution (the values of x) are x=-3 and x=-1.

 

That means that either  (x+3)=0  or  (x+1)=0  or both.

 

The equation is:  (x+3)(x+1) = 0

 

The Standard Form of a quadratic equation is:    ax² + bx + c = 0

     where a, b, and c are constants and a≠0

 

To change (x+3)(x+1) = 0 into Standard Form, use F-O-I-L:

    (x+3)(x+1) = 0

    x² + x + 3x + 3 = 0

    x² + 4x + 3 = 0

Answer 2

The solution could be (x+3)(x+1) = x²+4x+3

 

You could also multiply this quadratic by any non-zero constant to create another quad that has the same solutions