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

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Final Answer: The equation has $Two irrational solutions$ .

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Step 1 ：Given the quadratic equation $x^{2} + 7 x - 2 = 0$ , 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 $b^{2} - 4 a c$ .

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 $Two irrational solutions$ .

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 solutionsx2+7x−2=0a) Two irrational solutionsb) One rational solutionc) Two non-real solutionsd) Two rational solutions

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