Quadratic Applications
Most of the problems in this chapter are not much different from the word problems in previous chapters. The only difference is that quadratic equations are used to solve them. Because quadratic equations usually have two solutions, some of these applied problems will have two solutions. Most will have only one-one of the ‘‘solutions’’ will be invalid. More often than not, the invalid solutions are easy to recognize.
Alfi Blog April 14, 2026 Admin Bandung IndonesiaQuadratic Applications
Most of the problems in this chapter are not much different from the word problems in previous chapters. The only difference is that quadratic equations are used to solve them. Because quadratic equations usually have two solutions, some of these applied problems will have two solutions. Most will have only one-one of the ‘‘solutions’’ will be invalid. More often than not, the invalid solutions are easy to recognize.
Rational Equations
Some rational equations (an equation with one or more fractions as terms) become quadratic equations once each term has been multiplied by the least common denominator. Remember, you must be sure that any solutions do not lead to a zero in any denominator in the original equation.
Alfi Blog April 13, 2026 Admin Bandung IndonesiaRational Equations
Some rational equations (an equation with one or more fractions as terms) become quadratic equations once each term has been multiplied by the least common denominator. Remember, you must be sure that any solutions do not lead to a zero in any denominator in the original equation.
Now that we can identify a, b, and c in the quadratic formula and can simplify the solutions, we are ready to solve quadratic equations using the formula.
Alfi Blog April 12, 2026 Admin Bandung IndonesiaNow that we can identify a, b, and c in the quadratic formula and can simplify the solutions, we are ready to solve quadratic equations using the formula.
The quadratic formula can be messy to compute when any of a, b, or c are fractions or decimals. You can get around this by multiplying both sides of the equation by the least common denominator or some power of ten.
Alfi Blog April 11, 2026 Admin Bandung IndonesiaThe quadratic formula can be messy to compute when any of a, b, or c are fractions or decimals. You can get around this by multiplying both sides of the equation by the least common denominator or some power of ten.
The Quadratic Formula
The other main approach to solving quadratic equations comes from the fact that x2 = k implies x = √k, –√k and a technique called completing the square. The solutions to ax2 + bx + c = 0 are:
The Quadratic Formula
The other main approach to solving quadratic equations comes from the fact that x2 = k implies x = √k, –√k and a technique called completing the square. The solutions to ax2 + bx + c = 0 are:
