Question

Which of the following statements are true about the equation

x² −6x+2=0?

A) The solutions are x=3+√7
B) The extreme value is at the point (7, -3).
C) The graph of the quadratic equation has a minimum value.
D) The solutions are x=-3+√7
E) The extreme value is at the point (3, -7).
F) The graph of the quadratic equation has a maximum value.

Answer 1

The solutions to the equation x² - 6x + 2 = 0 are x = 3 + √7 and x = 3 - √7.

Step-by-step explanation:

The given quadratic equation is x² - 6x + 2 = 0.

To determine the solutions or roots, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

1. a = 1, b = -6, and c = 2
2. Substitute the values into the formula: x = (-(-6) ± √((-6)² - 4(1)(2))) / (2(1))
3. Simplify: x = (6 ± √(36 - 8))/2
4. Simplify further: x = (6 ± √28)/2
5. Split into two solutions: x = (6 + √28)/2 and x = (6 - √28)/2
6. Simplify the square root: x = (6 + 2√7)/2 and x = (6 - 2√7)/2

Therefore, the correct solutions are x = 3 + √7 and x = 3 - √7.