Question

Order the correct steps to find the value of the discriminant in the equation X² + 14 = 7x.

a) Subtract 7x from both sides
b) Move 14 to the other side
c) Set the equation to zero
d) Identify coefficients and constants

Answer 1

To find the discriminant of X² + 14 = 7x, set the equation to zero, identify coefficients, calculate the discriminant using the formula Δ = b² - 4ac, simplify, and check the result. The discriminant is -7.

Step-by-step explanation:

The correct steps to find the value of the discriminant in the equation X² + 14 = 7x are:

1. Set the equation to zero by subtracting 7x from both sides, resulting in X² - 7x + 14 = 0.
2. Identify coefficients and constants where a = 1 (coefficient of X²), b = -7 (coefficient of x), and c = 14 (constant term).
3. Calculate the discriminant using the formula Δ = b² - 4ac.
4. Eliminate terms wherever possible to simplify the algebra.
5. Check the answer to see if it is reasonable.

In this case, the discriminant is Δ = (-7)² - 4(1)(14) = 49 - 56 = -7.