Digital PSAT Math Practice Question 311: Answer and Explanation

Question: 311

How many real solution(s) does this system of equations have?

\begin{array}{rcl} y & = & 2 x - 5 \\ y & = & 2 x^{2} + 4 \end{array}

Correct Answer: A

Explanation:

(A) Set the two equations equal to each other. Express the result as a quadratic equation:

2 x - 5 = 2 x^{2} + 4 \to 2 x^{2} - 2 x + 9 = 0

Plug these values for a, b, and c into the quadratic equation. The only solutions are imaginary:

\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{2 \pm \sqrt{4 - 4 \times 18}}{2 \times 2} = \frac{2 \pm i \sqrt{68}}{4}

Therefore, there are zero solutions.