Question

What are the zeros of the quadratic function f(x) = 2x² - 10x - 3?

O x = -2-√3¹ and x = -
2
O x=
O
1
52
-√37
8
and x
52
x = -√3¹ and x = =+
2
37
0 x = -√√ and x = =+
+
√31
2
√31
37
8
37
8

Answer 1

Explanation:

To find the zeros of the quadratic function f(x) = 2x² - 10x - 3, we need to solve for x when f(x) is equal to zero. The zeros are the values of x that make the function equal to zero.

So, we set f(x) = 0 and solve for x:

2x² - 10x - 3 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -10, and c = -3.

Now, let's plug in the values:

x = (-( -10) ± √((-10)² - 4 * 2 * (-3))) / 2 * 2

x = (10 ± √(100 + 24)) / 4

x = (10 ± √124) / 4

Now, we need to simplify √124:

√124 = √(4 * 31) = 2√31

So, the solutions for x are:

x = (10 + 2√31) / 4

and

x = (10 - 2√31) / 4

Now, we can further simplify these solutions:

x = 5 + √31

and

x = 5 - √31

So, the zeros of the quadratic function f(x) = 2x² - 10x - 3 are x = 5 + √31 and x = 5 - √31.