Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.

Assessment: WAEC SSCE - Further Mathematics - 2018 (Objective) Subject: Further Mathematics

Question 1 Report

1, 3

-1, -3

1, -3

-1, 3

Answer Details

To find the values of x where the function f(x) is equal to 3, we need to solve the equation:

3x^2 - 12x + 12 = 3

We can start by subtracting 3 from both sides:

3x^2 - 12x + 12 - 3 = 3 - 3
3x^2 - 12x + 9 = 0

Next, we can use the quadratic formula to find the solutions for x:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 3, b = -12, c = 9. Plugging in these values, we get:

x = (-(-12) ± √((-12)^2 - 4 * 3 * 9)) / 2 * 3
x = (12 ± √(144 - 108)) / 6
x = (12 ± √36) / 6
x = (12 ± 6) / 6

So, the two values of x that solve the equation are:

x = (12 + 6) / 6 = 18 / 6 = 3
x = (12 - 6) / 6 = 6 / 6 = 1

Therefore, the two values of x that make f(x) equal to 3 are 1 and 3.

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