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Since the discriminant is 0, there is 1 real solution to the equation. b 2 − 4 a c Substitute in the values of a, b, and c. a = 9, b = −6, c = 1 Write the discriminant. 36 − 36 0 9 y 2 − 6 y + 1 = 0 The equation is in standard form, identify a, b, and c. Since the discriminant is negative, there are 2 complex solutions to the equation.ĩ y 2 − 6 y + 1 = 0 The equation is in standard form, identify a, b, and c. a = 5, b = 1, c = 4 Write the discriminant. 1 − 80 −79 5 n 2 + n + 4 = 0 The equation is in standard form, identify a, b, and c.
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Since the discriminant is positive, there are 2 real solutions to the equation.ĥ n 2 + n + 4 = 0 The equation is in standard form, identify a, b, and c. a = 3, b = 7, c = −9 Write the discriminant. 49 + 108 157 3 x 2 + 7 x − 9 = 0 The equation is in standard form, identify a, b, and c. To determine the number of solutions of each quadratic equation, we will look at its discriminant.ģ x 2 + 7 x − 9 = 0 The equation is in standard form, identify a, b, and c. We start with the standard form of a quadratic equation and solve it for x by completing the square. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier.
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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’. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Solve Quadratic Equations Using the Quadratic Formula If you missed this problem, review Example 8.76. If you missed this problem, review Example 8.13. If you missed this problem, review Example 1.21.
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\( \newcommand\)ĭetermine the number of solutions to each quadratic equation.