The following videos show how to use discriminants to determine the number of real solutions to quadratic equations. ![]() 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. ![]() 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. Also, especially in the beginning, put the b. I teach my students to start with the discriminant, b2-4ac. We always have to start with a quadratic in standard form: ax2+bx+c0. So we want two numbers that multiply together to make 6, and add up to 7. This is a formula, so if you can get the right numbers, you plug them into the formula and calculate the answer (s). 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. With the quadratic equation in this form: Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b. 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.
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