![]() Mathematicians look for patterns when they. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this’ The answer is ‘yes’. by completing the square, ( x + 5) 2 16 so x ± 4 - 5 (from above) by the quadratic formula. You can see hints of this when you solve quadratics. a, b and c are left as letters, to be as general as possible. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. The quadratic formula actually comes from completing the square to solve ax2 + bx + c 0. The following videos show how to use discriminants to determine the number of real solutions to quadratic equations. Solve Quadratic Equations Using the Quadratic Formula. Hence, the required solution of the quadratic equation 2 x 2 + 8 x + 3 0 is x ± 5 2 2. identify the coefficients, , and, and plug them into the formula. ![]() Consider the quadratic equation, a x 2 + b x + c 0, a 0. Steps for Solving Quadratic Equations using the Quadratic Formula: write the equation in polynomial form and it set equal to zero. If the discriminant is negative, then there is no real solution.įor example, in the quadratic equation x 2 + x + 5 = 0, its discriminant is equals toī 2 − 4 ac = (1) 2 − 4(1)(5) = −19 which is negative and so the equation has no real solution. Steps to Solve Quadratic Equation by Completing the Square Method. If the discriminant is zero, then there is exactly one real solution.įor example, in the quadratic equation x 2 + 4 x + 4 = 0, its discriminant is equals toī 2 − 4 ac = (4) 2 − 4(1)(4) = 0 and so the equation has exactly one real solution. If the discriminant is positive then there are two distinct solutions.įor example, in the quadratic equation 4 x 2 + 26 x + 12 = 0, its discriminant is equals to b 2 − 4 ac = (26) 2 − 4(4)(12) = 484 which is positive and so the equation has two real solutions. The number of solutions is determined by the discriminant. Quadratic equations can have two real solutions, one real solution or no real solution. In the quadratic formula, the expression under the square root sign, which is b 2 − 4 ac, is called the discriminant of the quadratic equation. Using the Discriminant to find number of solutions The following video shows how to use the quadratic formula to find solutions to quadratic equations. ![]() Putting the values into the formula, we get Where the notation ± is shorthand for indicating two solutions: one that uses the plus sign and the other that uses the minus sign.įind the solutions for the quadratic equation: 4 x 2 + 26 x + 12 = 0įrom the equation, we get a = 4, b = 26 and c = 12. When such an equation has solutions, they can be found using the quadratic formula: Where a, b, and c are real numbers and a ≠ 0. You can read this formula as: Where a 0 and b 2 4 a c 0. Using the Discriminant to find the number of SolutionsĪ quadratic equation in the variable x is an equation that can be written in the form Quadratic formula is used to solve any kind of quadratic equation.Solve Quadratic Equations using the Quadratic Formula.This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. ![]()
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