Algebra Know-It-ALL

576 Final Exam

(c) a ratio of an integer to a positive integer.

(d) a ratio of an integer to 1.

(e) a terminating decimal.

118. If the discriminant in a quadratic equation is a positive real number, it means that
     (a) the equation has two different real roots.
     (b) the equation has one real root with multiplicity 2.
     (c) the equation has one imaginary root with multiplicity 2.
     (d) the equation has two different imaginary roots.
     (e) the equation has no roots at all, real or imaginary.


119. Consider the following cubic equation in binomial-trinomial form:

(x− 5)(x^2 + 2 x+ 1) = 0

One of the real roots of this equation has multiplicity 2. Which one?

(a) The root x= 5.

(b) The root x=−5.

(c) The root x= 0.

(d) The root x= 1.

(e) The root x=−1.

120. Consider the following quadratic equation, which is expressed as a product of
     trinomials:

(x+ 2 −j5)(x+ 2 +j5)= 0

What is the solution set X for this equation?

(a)X= {(− 2 −j5), (− 2 +j5)}

(b)X= {(2 −j5), (2 +j5)}

(c)X= {2, −5}

(d)X= {j2,−j5}

(e) None of the above

121. Suppose that a 1 ,a 2 ,b 1 ,b 2 ,c 1 , and c 2 are real numbers, and neither a 1 nor a 2 are equal
     to 0. Consider

y=a 1 x^2 +b 1 x+c 1

and

y=a 2 x^2 +b 2 x+c 2