Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
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The document explains how to solve quadratic equations using the quadratic formula, x = −b ± √(b²−4ac) / 2a, where a, b, and c are coefficients. It outlines the steps required to apply the formula, including writing the equation in standard form, identifying coefficients, substituting values, and simplifying to find solutions. An example demonstrates this process with a specific quadratic equation.
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Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
- 1. Solving Quadratic Equations using Quadratic Formula
- 2. Quadratic Formula x = −b ± b2 − 4ac 2a Where: a, b, c are real numbers and a ≠0
- 3. If a quadratic equation is in the form of ax2 + bx + c = 0, you can use the values of a, b, and c to find the solution of the equations. That is, you can find those values of x that will make the equation true by using the quadratic formula
- 4. Quadratic Formula x = −b + b2 − 4ac 2a x = −b − b2 − 4ac 2a
- 5. Steps in solving Quadratic Equations using the Quadratic Formula 1. Write the equation in stand form (zero on one side of the equation) 2. List the numerical values of the coefficients a, b, and c. 3. Write the quadratic formula 4. Substitute the numerical values for a, b and c in the quadratic formula 5. Simplify to get the exact solution 6. Check your solution
- 6. Example: 9x2 - 14x + 4 = 0 x = −b ± b2 − 4ac 2a = −(−12)± (−12)2−4 9 4 2(9) Substitute for 9 for a, -12 for b, and 4 for c = 12± 144−144 18 Simplify = 12± 0 18 Simplify the Radical