Given f(x) = 1 + 4x − 3x^2, what are the values of x when f(x) = −3?
To find the values of x when f(x) = -3, we set f(x) equal to -3 and solve for x.
1 + 4x - 3x^2 = -3
Adding 3 to both sides of the equation:
4x - 3x^2 = -4
Rearranging the equation:
3x^2 - 4x + 4 = 0
To solve this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 3, b = -4, and c = 4.
Plugging in the values:
x = (-(-4) ± √((-4)^2 - 4(3)(4))) / 2(3)
= (4 ± √(16 - 48)) / 6
= (4 ± √(-32)) / 6
Since the square root of a negative number is not a real number, there are no real solutions for x when f(x) = -3.