Question 7 (1 point)
Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions or two non-real solutions
\[
x^{2}+7 x-2=0
\]
a) Two irrational solutions
b) One rational solution
c) Two non-real solutions
d) Two rational solutions

Step 1 ：Given the quadratic equation \(x^{2}+7x-2=0\), we can identify the coefficients as \(a = 1\), \(b = 7\), and \(c = -2\).

Step 2 ：The discriminant of a quadratic equation is given by the formula \(b^2 - 4ac\).

Step 3 ：Substitute the values of \(a\), \(b\), and \(c\) into the formula, we get the discriminant as 57.

Step 4 ：Since the discriminant is greater than 0, the equation has two distinct real solutions.

Step 5 ：However, a solution is rational if and only if the discriminant is a perfect square. In this case, 57 is not a perfect square, so the solutions must be irrational.

Step 6 ：Final Answer: The equation has \(\boxed{\text{Two irrational solutions}}\).