Question

Describe the nature of the roots for this equation.

2x² + 5x-7=0
OA. Two non-real roots
OB. Two real, irrational roots
OC. Two real, rational roots
OD. One real, double root

Answer 1

OC. Two real, rational roots is the answer

Answer 2

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.