Question 20

The solutions to the equation x² - 10 are ±√10.

The equation x² - 10 = 0 can be solved by isolating x², resulting in x² = 10. Taking the square root of both sides yields the solutions ±√10.

A) ±5

This option is incorrect because the solutions to the equation x² - 10 = 0 are found by taking the square root of 10, not 25. The values ±5 would result from the equation x² - 25 = 0.

B) ±√10

This option is correct as it directly reflects the solutions derived from the equation x² = 10. The roots of this equation are indeed ±√10, making this option accurate.

C) ±10

This choice is incorrect because it suggests that the solutions to the equation x² - 10 = 0 are ±10. The correct solutions involve the square root of 10, not the values of 10 itself.

D) ±10²

This option is incorrect as it implies the solutions are ±100. The term 10² equals 100, which does not correspond to the correct solutions of the original equation.

E) ±20

This choice is also incorrect. The value ±20 does not relate to the equation x² - 10 = 0, as the correct solutions are based on the square root of 10, not a linear transformation.

Conclusion

The correct answer is ±√10, as this directly solves the equation x² - 10 = 0. All other options fail to reflect the proper isolation of x² and the subsequent square root operation required to find the true solutions. Thus, understanding how to manipulate quadratic equations is essential for identifying accurate solutions.