solving quadratic equations by factoring examples

SOLVING QUADRATIC EQUATIONS BY FACTORING EXAMPLES PLUS

Find the radius of a cylinder whose volume is 2512 cubic centimeters and whose height is 8 centimeters. Find the -height of a cylinder if the volume is 282.6 in. Find the volume of a cylinder with a radius of 6 in. PI = 3.14 ( 3.14 is an approximation for PI)ġ.

The volume of a cylinder is given by the formula: V=PIr^2h The ﬁrst integer is 12 and the next consecutive even integer is 14. N=12 The problem asked for positive integers. (90 + 90 + 72 = 252, 180 + 36 + 36 = 252.ĥ. The sum of the squares of two positive consecutive even integers is 340. The length is 90 feet and the width is 72 feet, or the length is 180 feet and the Width is 36 feet. Since only three sides of the lot are involved, if one of the two equal sides is x, then 252-2x will be the third side. If 252 feet of fencing are needed and the area of the lot is 6480 square feet, what are the dimensions of the lot? The width is 9 9 meters and the length is 15 meters. ( (9*15=135))Ĥ. A man wants to build a block wall along three sides of his property.

SOLVING QUADRATIC EQUATIONS BY FACTORING EXAMPLES PLUS

Since the perimeter is 48 meters, then the length plus the Width must The perimeter of a rectangle is given by P = 2l + 2w. The area of a rectangle is the product of its length and width What are the dimensions of the rectangle? X=14 Extraneous solution because -29 does not ﬁt the conditions of the problem even though -29 is a solution to the equation.ģ. A rectangle has an area of 135 square meters and a perimeter of 48 meters. How many rows are there if there are 406 trees in the grove? X^2+4x-140=0 The constant factor 2 dues not More general problems and approaches to solving quadratic equations are discussed in Chapter 10.ġ. One number is four more than another, and the sum of their squares is 296. The problems in this section are set up so the equations can be solved by factoring. Several types of problems lead to quadratic equations. Check your solution with the wording of the problem to be sure it makes sense. (Possibly a formula of some type is necessary.)Ħ. Decide what is asked for and assign a variable to the unknown quantity.ģ. Organize a chart, or a table, or a diagram relating all the information provided.Ĥ. Form an equation. Read the problem carefully at least twice.Ģ. Word problems should be approached in an orderly manner. “What information is given? ” “What am I trying to ﬁnd? ” and “What tools, skills, and abilities do I need to use?.” You are to know from the nature of the problem what to do. Most problems do not say speciﬁcally to add, subtract, multiply, or divide. A problem that is easy for you, possibly because you have had experience in a particular situation, might be quite difficult for a friend, and vice versa. These abilities are developed over a long period of time. Whether or not word problems cause you difﬁculty depends a great deal on your personal experiences and general reasoning abilities. If there is more than one denominator, multiply by the LCM of the denominators.

Click on 'Solve Similar' button to see more examples.ģ*x^2/3+3*5x-3*18=3*0 Multiply each term on both sides of the equation by 3. Let’s see how our equation solver solves this and similar problems. Since both factors are the same, there is only one solution.Ĥ(x-3)(x+2)=0 The constant factor 4 can never be 0 and does not affect the solution. X^2+9x-22=0 One side of the equation must be 0. Solve the following quadratic equations by factoring. Using techniques other than factoring to solve quadratic equations is discussed in Chapter 10. Not all quadratics can be factored using integer coefficients. Each of these solutions is a solution of the quadratic equation. Putting each factor equal to 0 gives two ﬁrst-degree equations that can easily be solved. Equations of the formįactoring the quadratic expression, when possible, gives two factors of ﬁrst degree. Polynomials of second degree are called quadratics. The reason is that a product is 0 only if at least one of the factors is 0. Thus, to solve an equation involving a product of polynomials equal to 0, we can let each factor in turn equal 0 to ﬁnd all possible solutions.

Since we have a product that equals 0, we allow one of the factors to be 0. This procedure does not help because x^2-5x+6=0 is not any easier to solve than the original equation. Now consider an equation involving a product of two polynomials such as But did you think that x - 2 had to be 0? This is true because 5 * 0 = 0, and 0 is the only number multiplied by 5 that will give a product of 0. How would you solve the equation 5(x-2)=0? Would you proceed in either of the following ways?īoth ways are correct and yield the solution x = 2. 5.4 Solving Quadratic Equations by Factoring

Solving quadratic equations by factoring examples