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Solving Quadratic Equations
…by Factoring
Solving Quadratic Equations by Factoring
• Get ZERO on one side by itself.
• Factor. Consider Common Factors FIRST!
• Set each factor = 0.
• Solve each part.
Solve by factoring.
Answer: The solution set is {0, –4}.
Original equation
Add 4x to each side.
Factor the binomial.
Solve the second equation.
Zero Product Propertyor
Check Substitute 0 and –4 in for x in the original equation.
Solve by factoring.
Original equation
Subtract 5x and 2 from each side.
Factor the trinomial.
Zero Product Propertyor
Solve each equation.
Answer: The solution set is Check each solution.
Solve each equation by factoring.
a.
b.
Answer: {0, 3}
Answer:
Answer: The solution set is {3}.
Solve by factoring.
Original equation
Add 9 to each side.
Factor.
Zero Product Propertyor
Solve each equation.
CheckThe graph of the related function, intersects the x-axis only once. Since the zero of the function is 3, the solution of the related equation is 3.
Answer: {–5}
Solve by factoring.
Multiple-Choice Test Item What is the positive solution of the equation ?A –3 B 5 C 6 D 7
Read the Test Item
You are asked to find the positive solution of the given quadratic equation. This implies that the equation also has a solution that is not positive. Since a quadratic equation can either have one, two, or no solutions, we should expect this equation to have two solutions.
Solve the Test Item
Answer: D
Both solutions, –3 and 7, are listed among the answer choices. However, the question asks for the positive solution, 7.
Original equation
Factor.
Divide each side by 2.
Factor.
or Zero Product Property
Solve each equation.
Multiple-Choice Test Item What is the positive solution of the equation ?A 5 B –5 C 2 D 6
Answer: C
Write a quadratic equation with and 6 as its
roots. Write the equation in the form
where a, b, and c are integers.
Write the pattern.
Simplify.
Replace p with and q with 6.
Use FOIL.
Multiply each side by 3 so that b is an integer.
Answer: A quadratic equation with roots and 6
and integral coefficients is
You can check this result by graphing the
related function.
Write a quadratic equation with and 5 as its
roots. Write the equation in the form
where a, b, and c are integers.
Answer:
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