194k views
5 votes
Solve the equation and check it with the theorem of Vieta:

x^2 - 5√2x + 12 = 0
A) x = 2√2, 3√2
B) x = 5√2, -2√2
C) x = -2√2, -3√2
D) x = 3√2, 2√2

User Samuel
by
8.4k points

1 Answer

4 votes

Final answer:

The quadratic equation x² - 5√2x + 12 = 0 can be solved using the quadratic formula, yielding the solutions x = 3√2 and x = 2√2, which satisfy Vieta's theorem. The correct option is D.

Step-by-step explanation:

To solve the equation x² - 5√2x + 12 = 0, we can apply the quadratic formula, which is -b ± √b² - 4ac over 2a. Here, a = 1, b = -5√2, and c = 12.

Let us use the quadratic formula:

x = (-(-5√2) ± √(-5√2)² - 4(1)(12)) / (2(1))
= (5√2 ± √(50 - 48)) / 2
= (5√2 ± √2) / 2

The two solutions for x are therefore x = 3√2 and x = 2√2.

To check these solutions with Vietas' theorem, we should have the sum of the roots = -b/a (here it should be 5√2) and the product of the roots = c/a (here it should be 12). For our solutions,
Sum of the roots = 3√2 + 2√2 = 5√2
Product of the roots = 3√2 × 2√2 = 6∙ 2 = 12
This confirms that the solutions are correct and Vieta's theorem is satisfied. The correct answer option is D).

User Christok
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories