Question

Select the two values of x that are roots of this equation.
x² + 3x- 5=0

Answer 1

The two roots of the quadratic equation x² + 3x - 5 = 0 are found using the quadratic formula; they are approximately x ≈ 2.192 and x ≈ -5.192.

Step-by-step explanation:

The equation x² + 3x - 5 = 0 is a quadratic equation, and we can find its roots using the quadratic formula. For an equation of the form ax² + bx + c = 0, the quadratic formula is:

x = √((-b ± √(b² - 4ac)) / (2a))

In this case, a = 1, b = 3, and c = -5. Plugging these into the formula gives:

x = √((-3 ± √((3²) - 4(1)(-5))) / (2(1)))

x = √((-3 ± √(9 + 20)) / 2)

x = √((-3 ± √(29)) / 2)

So, the two roots of the equation are:

1. x = (-3 + √29) / 2
2. x = (-3 - √29) / 2

The calculated values (approximately):

• x ≈ 2.192
• x ≈ -5.192