Answer:
The equation 2x² + 5x - 7 = 0 can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For this equation, a = 2, b = 5, and c = -7. Substituting these values into the quadratic formula:
x = (-(5) ± √((5)² - 4(2)(-7))) / (2(2))
= (-5 ± √(25 + 56)) / 4
= (-5 ± √(81)) / 4
The discriminant, b² - 4ac, is 81. Since the discriminant is positive, the equation has two real roots.
The square root of 81 is 9, so the equation becomes:
x = (-5 ± 9) / 4
Simplifying further:
x1 = (-5 + 9) / 4 = 4/4 = 1
x2 = (-5 - 9) / 4 = -14/4 = -7/2 = -3.5
Therefore, the equation has two real, rational roots: x = 1 and x = -3.5.
The answer is (OC) Two real, rational roots.