How many real solutions are there for 5×^2+7×+2?
A. 0
B. 1
C. 2
D. 3
1 answer
We can use the quadratic formula to find the solutions: \[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}.\] For the equation $5x^2 + 7x + 2$, we have $a=5$, $b=7$, and $c=2$. Substituting these values into the quadratic formula, we get \[x = \frac{-7 \pm \sqrt{7^2 - 4(5)(2)}}{2(5)}.\] Simplifying inside the square root gives \[x = \frac{-7 \pm \sqrt{49-40}}{10} = \frac{-7 \pm \sqrt{9}}{10}.\] So we see that there are two real solutions: \[x = \frac{-7 + 3}{10} = \frac{-4}{10} = -\frac{2}{5} \quad \text{and} \quad x = \frac{-7 - 3}{10} = \frac{-10}{10} = -1.\] Thus, the answer is $\boxed{\text{(C) } 2}$.