To find the zeros of the quadratic function f(x) = 2x² + 10x + 3, we need to set the function equal to zero and solve for x:
2x² + 10x + 3 = 0
We can use the quadratic formula x = (-b ± √(b² – 4ac)) / (2a), where a, b, and c are the coefficients from the equation ax² + bx + c. For our function:
- a = 2
- b = 10
- c = 3
Now, we can calculate the discriminant (b² – 4ac):
b² – 4ac = 10² – 4(2)(3) = 100 – 24 = 76
Since the discriminant is positive, we will have two distinct real zeros. Now we can plug in the values into the quadratic formula:
x = (-10 ± √76) / (2 * 2)
This simplifies to:
x = (-10 ± 2√19) / 4
Which further simplifies to:
x = -5/2 ± √19/2
Therefore, the zeros of the quadratic function f(x) = 2x² + 10x + 3 are:
- x = -5/2 + √19/2
- x = -5/2 – √19/2