Question

Select the two values of x that are roots of this equation.

[ x² + 3x - 6 = 0 ]

a) ( x = -3 + √15 )
b) ( x = -3 - √15 )
c) ( x = -3 + √15/2 )
d) ( x = -3 - √15/2 )

Answer 1

The values of x that are roots of the equation x² + 3x - 6 = 0 are (-3 + √33) / 2 and (-3 - √33) / 2.

Step-by-step explanation:

The equation given is x² + 3x - 6 = 0. To find the values of x that are the roots of this equation, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values a = 1, b = 3, and c = -6 into the formula, we get:

x = (-3 ± √(3² - 4(1)(-6))) / (2(1))

Simplifying the equation, we obtain:

x = (-3 ± √(9 + 24)) / 2

x = (-3 ± √33) / 2

Therefore, the two values of x that are roots of the equation are x = (-3 + √33) / 2 and x = (-3 - √33) / 2.