# Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 178: 54

The given equation has one rational solution (with multiplicity 2).

#### Work Step by Step

The given equation has $a=25$, $b=110$, and $c=121$. RECALL: (1) The discriminant is equal to $b^2-4ac$. (2) A quadratic equation has the following types of solutions based on the value of the discriminant: (a) when $b^2-4ac\gt0$, the equation has two unequal rational solutions; (b) when $b^2-4ac=0$, the equation has one, repeated rational solution; and (c) when $b^2-4ac\lt0$, the equation has two complex number solutions; The discriminant of the equation above is: $$b^2-4ac =110^2 - 4(25)(121) = 12,100-12,100=0$$ The discriminant is zero. Thus, the given equation has one rational solution (with multiplicity 2).

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