Problem Solving With Quadratic Equations Essay On Practicality
Since I'll be cutting equal-sized squares out of all of the corners, and since the box will have a square bottom, I know I'll be starting with a square piece of cardboard.In this last exercise above, you should notice that each solution method gave the same final answer for the cardboard's width.Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula.When we solved linear equations, if an equation had too many fractions we ‘cleared the fractions’ by multiplying both sides of the equation by the LCD.
Yes, the quantity inside the radical of the Quadratic Formula makes it easy for us to determine the number of solutions.
We cannot take the square root of a negative number.
So, when we substitute , , and into the Quadratic Formula, if the quantity inside the radical is negative, the quadratic equation has no real solution. The quadratic equations we have solved so far in this section were all written in standard form, .
We will see in the next example how using the Quadratic Formula to solve an equation with a perfect square also gives just one solution.
When we solved the quadratic equations in the previous examples, sometimes we got two solutions, sometimes one solution, sometimes no real solutions.