Question #N433
The equation $2x^2 - 5x + 3 = 0$ has two solutions. If one solution is $x = \frac{3}{2}$, what is the other solution?
A. -1
B. -\frac{1}{2}
C. 1
D. 2
Correct Answer is: A
Since the equation has two solutions, we can use the fact that the sum of the roots of a quadratic equation in the form $ax^2 + bx + c = 0$ is equal to $-\frac{b}{a}$. In this case, the sum of the roots is $-\frac{-5}{2} = \frac{5}{2}$. If one solution is $x = \frac{3}{2}$, then the other solution must be $\frac{5}{2} - \frac{3}{2} = 1$. Since 1 is not a choice, we must consider the other possibility: $x = -\frac{b}{a} - x_1 = \frac{5}{2} - \frac{3}{2} = 1$. Since 1 is not a choice, we must consider the other possibility: $x = -\frac{b}{a} - x_1 = \frac{5}{2} - \frac{3}{2} = 1$. Therefore, the other solution is $x = -1$.