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:
Sometimes
using the fact that x2 = k implies x = ±√k can be used to solve quadratic
equations. For instance, if x2 = 9, then x = 3 or –3 because 32
= 9 and (–3)2 = 9. This method works if the equation can be put in
the form ax2 – c = 0, where a and c are not negative.
Sometimes
using the fact that x2 = k implies x = ±√k can be used to solve quadratic
equations. For instance, if x2 = 9, then x = 3 or –3 because 32
= 9 and (–3)2 = 9. This method works if the equation can be put in
the form ax2 – c = 0, where a and c are not negative.
