Question

Derive the quadratic formula by selecting the appropriate pulldowns for j, k, l, m, n, p, and q.

a) j = -b, k = ±, l = sqrt(b^2 - 4ac), m = 2a, n = a, p = 2, q = c
b) j = b, k = ±, l = sqrt(b^2 - 4ac), m = 2a, n = a, p = 2, q = c
c) j = -b, k = ∓, l = sqrt(b^2 + 4ac), m = 2a, n = a, p = 2, q = -c
d) j = b, k = ∓, l = sqrt(b^2 + 4ac), m = 2a, n = a, p = 2, q = -c

Answer 1

To derive the quadratic formula for quadratic equations of the form ax²+bx+c = 0, we complete the square and solve for x. The correct derivation utilizes the values j = -b, k = ±, l = √(b² - 4ac), and m = 2a.

So option (A) is the correct answer.

Step-by-step explanation:

The quadratic formula is used to solve any quadratic equation of the form ax²+bx+c = 0. The formula for the roots of this equation is given by:

x = −b ± √(b² − 4ac)/(2a)

To derive the quadratic formula, we complete the square in the general form of a quadratic equation and solve for x. The correct values to plug into the quadratic formula are j = −b, k = ±, l = √(b² − 4ac), and m = 2a. Therefore, the correct choice from the given options is a), which follows the standard form of the quadratic formula.

For example, if we have constants a = 3, b = 13, and c = -10. Substituting these values into the quadratic formula results in:

x = −(13) ± √((13)² − 4 × 3 × (−10))/(2 × 3)

The solutions to this expression are the roots of the quadratic equation with the given coefficients.