a.
To find: Whether the method of factoring can be used to solve the
a.
Answer to Problem 60E
The method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are integers.
Explanation of Solution
Consider the quadratic equation be
Write the factors of the above equation using the factorization method as:
So, the solutions of the equation are
It is seen that the solution of the equation is obtained by factorization method.
Hence, the method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are integers.
b.
To find: Whether the method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are fractions.
b.
Answer to Problem 60E
The method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are fractions.
Explanation of Solution
Consider the quadratic equation be
Write the factors of the above equation using the factorization method as:
So, the solutions of the equation are
It is seen that the solution of the equation are fractions and the solutions can be obtained by factorization method.
Hence, the method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are fractions.
c.
To write: The generalization about quadratic equations with rational numbers.
c.
Answer to Problem 60E
A quadratic equation with rational solutions can be solved by using factorization or quadratic formula.
Explanation of Solution
Consider the quadratic equation be
Write the factors of the above equation using the factorization method as:
So, the solutions of the equation are
It is seen that the solution of the equation are fractions and the solutions can be obtained by factorization method.
Thus, the method of factoring can be used to solve the quadratic equation if the solutions obtained from the equation are rational numbers.
Hence, a quadratic equation with rational solutions can be solved by using factorization or quadratic formula.
Chapter 9 Solutions
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