Question

Solve the quadratic equation (x²+4√3x+12=0) using the pointer tool to estimate and select the approximate solution.

a) (x ≈ -6)
b) (x ≈ -3)
c) (x ≈ 2)
d) (x ≈ 6)

Answer 1

The quadratic equation (x²+4√3x+12=0) is solved using the quadratic formula, which yields one real solution since the discriminant is zero. The solution is estimated to be (x ≈ -3) based on the approximation of √3.

Step-by-step explanation:

To solve the quadratic equation (x²+4√3x+12=0), we can use the quadratic formula, which is -b ± √b² - 4ac / 2a. In our equation, a = 1, b = 4√3, and c = 12. Plugging these values into the quadratic formula, we get:

x = -4√3 ± √(4√3)² - 4(1)(12) / (2 * 1)

Simplifying further:

x = -4√3 ± √(48 - 48) / 2

x = -4√3 / 2

Since the discriminant (the value under the square root) is zero, there is only one real solution to the equation, which is:

x = -2√3

Estimating the value of √3 as approximately 1.732, we get:

x ≈ -2(1.732)

x ≈ -3.464

Thus, the approximate solution to the equation is (x ≈ -3).