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Learn various methods such as factoring, completing the square, and using the quadratic formula to solve quadratic equations easily and efficiently. Understand when each method is most suitable.
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EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x2 – 7 = 0 SOLUTION a. The quadratic equation can be solved using square roots because the equation can be written in the form x2=d.
EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). b.x2 + 4x = 0 SOLUTION b. The equation can be solved by factoring because the expression x2+4x can be factored easily. Also, the equation can be solved by completing the square because the equation is of the form ax2+bx+c=0 where a=1 and b is an even number.
EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). c. 5x2 + 9x – 4 = 0 SOLUTION c. The quadratic equation cannot be factored easily, and completing the square will result in many fractions. So, the equation can be solved using the quadratic formula.
for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 5. x2 + x – 6 = 0 SOLUTION Factoring because the expression factors easily.
for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 6. x2 – 9 = 0 SOLUTION Factoring because the expression factors easily. Using square roots is another option since the equation can be written in the formx2 = d.
for Example 4 GUIDED PRACTICE Tell what method you would use to solve the quadratic equation. Explain your choice(s). 7. x2 + 6x = 5 SOLUTION Completing the square because the equation is of the form ax2 + bx = c where a = 1 and b is an even number. Another method is the quadratic formula since the equation does not factor easily.
