Question

Solve the equation by using the quadratic formula: 2x^2 + 13x = 0.

Option a: x = 13/2, 0
Option b: x = -13/2, 0
Option c: x = ±13/2
Option d: x = 0

Answer 1

The equation 2x² + 13x = 0 is solved using the quadratic formula and gives two solutions: x = 0 and x = -13/2, matching option b.

Step-by-step explanation:

To solve the equation 2x2 + 13x = 0 using the quadratic formula, we first need to express the equation in the standard quadratic form ax2 + bx + c = 0. In this case, the equation is already set to 0, and we identify a = 2, b = 13, and c = 0. The quadratic formula is x = (-b ± √(b2 - 4ac)) / (2a).

Substituting the values into the formula, we get:

x = (-13 ± √(132 - 4 × 2 × 0)) / (2 × 2)

Which simplifies to:

x = (-13 ± √(169)) / 4

x = (-13 ± 13) / 4

This gives us two solutions:

• x = 0 (since -13 + 13 = 0)
• x = -13 / 4, which simplifies to x = -13/2

Thus, the solutions are x = 0 and x = -13/2, which corresponds to option b.