f(x)=-3x²-14x=24
find the zeros of the polynomial function
Use the quadratic equation to solve
3x^2 + 14x + 24 = 0
Both roots will be complex, since b^2 - 4ac = -92 < 0 .
To find the zeros of a polynomial function, we need to solve the equation f(x) = 0. In this case, the given polynomial equation is f(x) = -3x² - 14x + 24.
Step 1: Rewrite the equation in standard form (ax² + bx + c = 0).
By moving all the terms to one side, we get:
-3x² - 14x + 24 = 0
Step 2: Factor or use the quadratic formula to solve for x.
In this case, we will use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Comparing the equation to ax² + bx + c = 0, we have:
a = -3, b = -14, c = 24
Now, substituting these values into the quadratic formula, we get:
x = (-(-14) ± √((-14)² - 4(-3)(24))) / (2(-3))
x = (14 ± √(196 + 288)) / -6
x = (14 ± √484) / -6
x = (14 ± 22) / -6
Step 3: Simplify the expression.
x₁ = (14 + 22) / -6 = 36 / -6 = -6
x₂ = (14 - 22) / -6 = -8 / -6 = 4/3
Therefore, the zeros of the polynomial function f(x) = -3x² - 14x + 24 are x = -6 and x = 4/3.