Solve for the zeros of the function using the quadratic formula.
3x^2=-4x+6
I know what the quadratic formula is but when I put it into the formula I keep getting an error on the graphing calculator.
The quadratic formula assume the equation to be:
ax²+bx+c=0
(i.e. all terms are on the left-side of the equation).
Rearrange the equation to be
3x²+4x-6=0
and try again.
You do not need a graphing calculator to find the zeroes. Either by hand, or a regular calculator will do.
To solve for the zeros of the quadratic function 3x^2 = -4x + 6, we can rearrange the equation to bring it into standard quadratic form (ax^2 + bx + c = 0), and then apply the quadratic formula.
1. Start by rearranging the equation:
3x^2 + 4x - 6 = 0
Now we have the quadratic equation in standard form.
2. Identify the values of a, b, and c:
In this equation, a = 3, b = 4, and c = -6.
3. Apply the quadratic formula:
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values of a, b, and c into the formula, we get:
x = (-4 ± √(4^2 - 4 * 3 * -6)) / (2 * 3)
Simplifying further:
x = (-4 ± √(16 + 72)) / 6
x = (-4 ± √88) / 6
Now, let's evaluate √88:
√88 = √(4 * 22) = 2√22
Now we can rewrite our equation:
x = (-4 ± 2√22) / 6
4. Simplify further:
x = (-2 ± √22) / 3
The equation x = (-2 ± √22) / 3 represents the two possible solutions (zeros) of the quadratic equation.