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Chapter 11: Problem 94

If you are given a quadratic equation, how do you determine which method to use to solve it?

Short Answer

Expert verified
To determine the method for solving a quadratic equation depend on the form of the quadratic equation and if it can be factored, if 'b' term is zero to apply square root method, if coefficient of x^2 is 1 and 'b' is even to complete the square, or for other cases, apply quadratic formula method. Choose the method that is simplest and most efficient for the specific equation.

Step by step solution

01

Identifying the form of the Quadratic Equation

A quadratic equation is any equation that can be rearranged in the form ax^2 + bx + c = 0 where a, b, and c are real numbers, and a 鈮� 0. The values of a, b and c will guide in choosing the best method to solve the equation.
02

Determining the solvable method using Factoring

If the quadratic can be factored, then factoring is the quickest and easiest method. This method is best used when the equation can be easily factored into two binomial terms.
03

Using the Square Roots Method

The square root method is best used when the quadratic equation has no 'b' term. In a scenario where b=0, the quadratic equation becomes a perfect square, and can be solved by taking the square root of both sides of the equation.
04

Solving by Completing the Square

Completing the square method becomes handy when the coefficient of x^2 (which is 'a') is 1 and 'b' is even. This method can be a little involved but it's advantageous when factoring is not straightforward.
05

Determining when to apply Quadratic Formula Method

When factoring, square root method, or completing the square doesn't work or is cumbersome, the Quadratic Formula method, -b 卤 鈭�(b^2-4ac) / 2a, can be applied. This method works for nearly all quadratic equations, but it can be more time-consuming than the other methods.

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Most popular questions from this chapter

Without going into specific details for every step, describe how the quadratic formula is derived.

Rationalize the denominator: \(\frac{5}{\sqrt{3}+x}\) (Section 10.5 Example 5 )

The annual yield per lemon tree is fairly constant at 320 pounds when the number of trees per acre is 50 or fewer. For each additional tree over \(50,\) the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. Find the number of trees that should be planted on an acre to produce the maximum yield. How many pounds is the maximum yield?

Solve each equation by the method of your choice. $$\frac{x-1}{x-2}+\frac{x}{x-3}=\frac{1}{x^{2}-5 x+6}$$

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.
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